SIMILAR CALL SIGNS CAUSED COM CONFUSION FOR 2 ACR FLCS AS WELL AS ATC CTLR. IN THIS INCIDENT THE RPTR FLC ANSWERED A DSCNT CLRNC FOR ANOTHER ACFT; BUT ATC FAILED TO NOTE THE ERROR IN CALL SIGN. THOUGH THE ACR'S WERE DIFFERENT; THEIR NUMERICAL NUMBERS STARTED WITH THE SAME FIRST NUMBERS AND ENDED WITH THE SAME NUMBER. CREATED COM DIFFICULTIES THROUGHOUT THE DSCNT AND APCH.

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WE WERE FLT ACR XX23 AND WERE ISSUED A CLRNC BY ZDC TO DSND FROM FL190 TO 16000 FT MSL. I READ BACK THIS CLRNC IN ITS ENTIRETY; INCLUDING OUR CALL SIGN ACR XX23. THE FO WAS FLYING AND STARTED TO DSND. AT FL183 CTR ASKED US WHAT OUR ALT WAS. I ANSWERED THAT WE WERE AT FL183 DSNDING TO 16000 FT AS CLRED; INCLUDING FULL CALL SIGN. CTR THEN TOLD US TO CLB TO FL190 WHICH WE DID. THE FO AND I HAD CLRLY UNDERSTOOD OUR CLRNC DOWN TO 16000 FT. SO I STATED TO ATC THAT WE HAD READ BACK OUR CLRNC TO 16000 FT INCLUDING OUR CALL SIGN ACR XX23 AND GOT AN ACKNOWLEDGEMENT FROM ZDC. (THERE WAS AN ACR XX63 ON FREQ.) SEVERAL TIMES DURING DSCNT AND LATTER PART OF ARR INTO DCA; CTR AND APCH CALLED US ACR XX63 INSTEAD OF XX23; READ BACK SOME OF THE XMISSIONS INTENDED FOR US. IT TOOK SEVERAL XMISSIONS AS WE WERE TRYING TO CLARIFY THAT WE WERE XX23. FINALLY APCH STARTED TO USE OUR CORRECT CALL SIGN AND WE COMPLIED WITH THESE DIRECTIONS. SEVERAL TIMES XX63 WOULD ANSWER FOR XX23. RECOMMENDATIONS: 1) TRY TO AVOID SIMILAR CALL SIGNS. 2) WE KNOW ATC IS BUSY BUT HAVE THEM LISTEN UP AND ACKNOWLEDGE XMISSIONS.