<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>0020 - Disclosure - 14. DARPA CONTRACT AND RELATED REVENUE RECOGNITION</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>From2012-04-01to2013-03-31</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000882291</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2012-04-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-03-31T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="12 Months Ended" /><Label Key="Calendar" Id="1" Label="Mar. 31, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>aemd_RecognizedRevenueDisclosureTextBlockAbstract</ElementName><ElementPrefix>aemd_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Darpa Contract And Related Revenue Recognition</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>aemd_DarpaContractAndRelatedRevenueRecognition</ElementName><ElementPrefix>aemd_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="From2012-04-01to2013-03-31" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;As discussed in Note 1, we entered into a government contract with
DARPA on September 30, 2011 and commenced work on such contract in October 2011. Originally, only the base year (year one contract)
was effective for the parties, however, effective August 16, 2012, DARPA exercised the option on the second year of the contract.&amp;#160;&amp;#160;Years
three through five are subject to DARPA exercising their option to enter into contracts for those years.&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;As a result of achieving five contract milestones between October
1, 2011 and March 31, 2012, we reported $1,358,189 in contract revenue for the fiscal year ended March 31, 2012. As a result of
achieving six milestones in the fiscal year ended March 31, 2013, we reported $1,230,004 in contract revenue for that fiscal year.&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;Originally, only the base year (year one contract covering October
1, 2011 through September 30, 2012) was effective for the parties, however, effective August 16, 2012, DARPA exercised the option
on the second year of the contract.&amp;#160;&amp;#160;Years three through five are subject to DARPA exercising their option to enter into
contracts for those years.&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;Year One Milestones&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;The year one contract (also referred to as &amp;#147;Year One&amp;#148;)
contained eight milestones of which five were achieved during the fiscal year ended March 31, 2012 and the remaining three were
achieved during the fiscal year ended March 31, 2012. The details of the eight Year One milestones achieved during the fiscal years
ended March 31, 2012 and 2013 were as follows:&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;Year One Milestones Achieved During Fiscal Year Ended March 31, 2012:&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;Milestone 2.2.1.1 &amp;#150; Write requirements definition for the extracorporeal
blood purification system and acquire necessary equipment with a milestone payment of $358,284. Management considers this milestone
to be substantive as it was not dependent on the passage of time nor was it based solely on another party's efforts.&amp;#160;&amp;#160;We
worked on this concept for a number of months beginning with a presentation to DARPA in late 2010.&amp;#160;&amp;#160;We subsequently filed
for IP protection on certain of the key concepts in March 2011 and our management visited selected potential vendors to work out
many of the details in the summer of 2011 before we were awarded the contract on September 30, 2011.&amp;#160;&amp;#160;We ordered the
breadboard device from one of our vendors before the milestone payment was made.&amp;#160;&amp;#160;We designed the breadboard prototype
and then presented the design to DARPA in order to achieve the milestone.&amp;#160;&amp;#160;The report was accepted by the contracting
officer's representative and the invoice was submitted thereafter.&amp;#160;&amp;#160;DARPA made the milestone payment in full.&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;Milestone 2.2.1.2 -- Fabricate breadboard prototypes for anticoagulation-free
anti-sepsis extracorporeal system (ASEPSYS) device. Fabricate prototype blood tubing sets. Acquire anti-thrombogenic surface modified
hollow fiber plasma separators with a milestone payment of $183,367. Management considers this milestone to be substantive as it
was not dependent on the passage of time nor was it based solely on another party's efforts.&amp;#160;&amp;#160;The consideration for this
milestone covers the cost of having the breadboard prototype developed to our specifications, hiring an engineer to supervise the
project, acquiring specially coated cartridges and associated overhead. The report was accepted by the contracting officer's representative
and the invoice was submitted thereafter.&amp;#160;&amp;#160;DARPA made the milestone payment in full.&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;Milestone 2.2.2.1 &amp;#150; Begin to develop the ADAPT device to efficiently
capture sepsis precursors and acquire important equipment and supplies with a milestone payment of $416,424. Management considers
this milestone to be substantive as it was not dependent on the passage of time nor was it based solely on another party's efforts.&amp;#160;&amp;#160;It
was critically important to obtain certain pieces of lab equipment as early as possible after winning the contract in order to
measure the binding ability of sepsis precursors.&amp;#160;&amp;#160;We demonstrated that we were able to capture one of the identified
possible sepsis precursors as part of our submission for approval.&amp;#160;&amp;#160;The consideration was also designed to cover the
salaries of new and existing scientists, lab space, materials as well as fringe and corporate overhead.&amp;#160;&amp;#160;The report was
accepted by the contracting officer's representative and the invoice was submitted thereafter.&amp;#160;&amp;#160;DARPA made the milestone
payment in full.&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;Milestone 2.2.2.2 - Perform initial screening of the different proposed
capture agents by measuring binding affinity and kinetics using surface plasmon resonance (SPR) or biolayer surface interferometry
(BLI) with a milestone payment amount of $216,747. Management considers this milestone to be substantive as it was not dependent
on the passage of time nor was it based solely on another party's efforts.&amp;#160;&amp;#160;We demonstrated that we were able to capture
several of the identified possible sepsis precursors as part of our submission for approval.&amp;#160;&amp;#160;The consideration was also
designed to cover the salaries of new and existing scientists, lab space, materials as well as fringe and corporate overhead.&amp;#160;&amp;#160;The
report was accepted by the contracting officer's representative and the invoice was submitted thereafter.&amp;#160;&amp;#160;DARPA made
the milestone payment in full.&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;Milestone&amp;#160;&amp;#160;2.2.1.3 - Assemble and test breadboard ASEPSYS
devices.&amp;#160;&amp;#160;Evaluate the use of different techniques and approaches to eliminating anticoagulants.&amp;#160;&amp;#160;The milestone
payment amount was $183,367.&amp;#160;&amp;#160;Management considers this milestone to be substantive as it was not dependent on the passage
of time nor was it based solely on another party's efforts.&amp;#160;&amp;#160;The consideration for this milestone covers the cost of
assembling and testing the breadboard prototype that we had developed to our specifications, hiring an engineer to supervise the
project, testing specially coated cartridges and associated overhead. The report was accepted by the contracting officer's representative
and the invoice was submitted thereafter.&amp;#160;&amp;#160;The report was accepted by the contracting officer's representative and the
invoice was submitted thereafter.&amp;#160;&amp;#160;DARPA made the milestone payment in full.&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;Year One Milestones Achieved During Fiscal Year Ended March 31, 2013:&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;Milestone 2.2.2.3 &amp;#150; Perform preliminary quantitative real time
PCR to measure viral load, and specific DNA or RNA targets. The milestone payment was $216,747. Management considers this milestone
to be substantive as it was not dependent on the passage of time nor was it based solely on another party's efforts. We demonstrated
that we were able to measure viral load of one or more targets as part of our submission for approval.&amp;#160;&amp;#160;The report was
accepted by the contracting officer's representative and the invoice was submitted thereafter.&amp;#160;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;Milestone 2.2.1.4 &amp;#150; Obtain all necessary IRB documentation
and obtain both institutional and Government approval in accordance with IRB documentation submission guidance prior to conducting
human or animal testing. The milestone payment was $183,367. Management considers this milestone to be substantive as it was not
dependent on the passage of time nor was it based solely on another party's efforts.&amp;#160;&amp;#160;We obtained all of the required
documentation from both institutional and Government authorities. The report was accepted by the contracting officer's representative
and the invoice was submitted thereafter.&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;Milestone M2 &amp;#150; Target capture &amp;#62; 50% in 24 hours for at least
one target in blood or blood components. The milestone payment was $216,747. Management considers this milestone to be substantive
as it was not dependent on the passage of time nor was it based solely on another party's efforts.&amp;#160;&amp;#160;We demonstrated that
we were able to capture &amp;#62; 50% in 24 hours of one of the agreed targets in blood or blood components. The report was accepted
by the contracting officer's representative and the invoice was submitted thereafter.&amp;#160;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;Year Two Milestones&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;The year two contract (also referred to as &amp;#147;Year Two&amp;#148;)
contained eight milestones of which three were achieved during the fiscal year ended March 31, 2013. The details of the three Year
Two milestones achieved during the fiscal year ended March 31, 2013 were as follows:&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;Milestone 2.3.3.1 &amp;#150; Build the ADAPT capture cartridges with
the identified affinity agents. Measure the rate of capture of the specific targets from in ex vivo recirculation experiments from
cell culture and blood. The milestone payment was $208,781. Management considers this milestone to be substantive as it was not
dependent on the passage of time nor was it based solely on another party's efforts.&amp;#160;&amp;#160;We demonstrated that we were able
build the ADAPT capture cartridges with the identified affinity agents and to measure the rate of capture of the specific targets
from in ex vivo recirculation experiments from cell culture and blood. The report was accepted by the contracting officer's representative
and the invoice was submitted thereafter.&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;Milestone 2.3.2.1 &amp;#150; &lt;font style="color: black"&gt;Demonstrate
the effectiveness of the prototype device in vivo in animals preventing platelet activation or clotting in at least a 2 hour blood
pumping experiment at 75 mL/min blood flow.&lt;/font&gt; &lt;font style="color: black"&gt;The milestone payment amount was $&lt;/font&gt;195,581.
Management considers this milestone to be substantive as it was not dependent on the passage of time nor was it based solely on
another party's efforts.&amp;#160;&amp;#160;The prototype device was successfully used &lt;font style="color: black"&gt;in vivo in animals preventing
platelet activation or clotting in at least a 2 hour blood pumping experiment at 75 mL/min blood flow.&lt;/font&gt; The report was accepted
by the contracting officer's representative and the invoice was submitted thereafter.&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 8pt Times New Roman, Times, Serif; margin: 0"&gt;Milestone M4 &amp;#150; Target capture &amp;#62; &lt;font style="color: black"&gt;50%
in 24 hours for at least 5 targets in blood or blood components.&lt;/font&gt; The milestone payment was $208,781. Management considers
this milestone to be substantive as it was not dependent on the passage of time nor was it based solely on another party's efforts.&amp;#160;&amp;#160;We
demonstrated that we were able to capture &amp;#62; 50% in 24 hours for at least 5 of the agreed targets in blood or blood components.
The report was accepted by the contracting officer's representative and the invoice was submitted thereafter.&amp;#160;&amp;#160;&lt;/p&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>Darpa Contract and Related Revenue Recognition text block</ElementDefenition><ElementReferences>No definition available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>DARPA CONTRACT AND RELATED REVENUE RECOGNITION</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>14. DARPA CONTRACT AND RELATED REVENUE RECOGNITION</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://aethlonmedical.com/role/DarpaContractAndRelatedRevenueRecognition</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
