B737-300 CREW AND SAME ACR WITH A SIMILAR CALL SIGN; HAD THE ZDC RADAR CTLR ISSUE A CLRNC TO THE WRONG ACFT IN ZDC CLASS A.

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FO FLYING; CAPT OPERATING RADIOS. LEVEL AT FL330; ZDC INSTRUCTS; 'ACR X; DSND AND MAINTAIN FL290.' THE CAPT READS BACK 'DSND TO FL290; ACR X.' AFTER CONFIRMING THE ALT WITH THE CAPT BY POINTING AT THE SELECTED ALT; I STARTED MY DSCNT. AFTER PASSING FL326; ATC INSTRUCTED US TO CLB BACK UP TO FL330; AS THE INSTRUCTION WAS FOR ACR Y. WE HAD BEEN FOLLOWING 'ACR Y FROM SOUTH FLORIDA AND WERE LISTENING CAREFULLY AS WE HAD SIMILAR CALL SIGNS. BOTH THE CAPT AND I CAN BE ASSURED THAT ATC CALLED 'ACR X AND NOT ACR Y.' AFTER ARRIVING IN PIT; I TALKED TO ZDC SUPVR WHO HAD NOT LISTENED TO THE TAPES YET BUT SAID THAT THEY (ZDC) HAVE BEEN HAVING TROUBLE WITH THE 2 CALL SIGNS FOR AWHILE. I SAID THAT I WOULD TALK TO DISPATCH TO SEE IF THEY COULD MAKE ANY MODIFICATIONS TO THE SIMILAR SOUNDING CALL SIGNS. AFTER HANGING UP WITH ATC; I CONTACTED DISPATCH; AS HE WAS AT THE DESK THAT ACR X WAS DISPATCHED FROM. HE NOTED THAT ACR Y DEPARTED PBI MINS BEFORE WE DEPARTED FLL AND HAD THE EXACT SAME RTE. HE MADE A NOTE TO HAVE THE CALL SIGNS ADJUSTED TO PREVENT FURTHER CONFUSION.