
<PAGE>   1
 
   
                                                                    EXHIBIT 23-A
    
 
   
                       CONSENT OF INDEPENDENT ACCOUNTANTS
    
 
   
We consent to the reference to our firm under the captions "Experts" and
"Selected Historical and Pro Forma Combined Financial Data" in the Amendment No.
3 to the Registration Statement on Form S-4 and related Joint Proxy
Statement/Prospectus of SBC Communications Inc. (SBC) for the registration of
shares of SBC Common Stock and to the incorporation by reference therein of our
reports dated February 9, 1996, with respect to the consolidated financial
statements and schedules of SBC included in or incorporated by reference in its
Annual Report (Form 10-K) for the year ended December 31, 1995, filed with the
Securities and Exchange Commission.
    
 
   
                                                   /s/  ERNST & YOUNG LLP
    
 
                                            ------------------------------------
 
   
San Antonio, Texas
    
   
June 3, 1996
    
