B717 EXPERIENCED LOSS OF SEPARATION AT FL290 WITH ZMA INVOLVING SIMILAR CALL SIGNS.

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WHILE ON ZMA (127.05) WE WERE ADVISED OF ACR WITH SIMILAR CALL SIGN ON FREQ (WE WERE ACR XXY). THEY WERE AHEAD OF US BY SEVERAL MI. WE WERE BOTH FLYING N AT FL290. WE WERE ADVISED TO TURN L 15 DEGS; CLB TO FL330 AND CONTACT ZMA ON 127.47. I THINK AT LEAST 2 RADIO XMISSIONS WERE INVOLVED; ALL TO ACR XXY. WE RESPONDED TO ALL CALLS AS ACR XXY AND ALWAYS ALLOWED A LENGTHY PAUSE TO ENSURE WE WERE THE CORRECT RESPONDENT. AT THE SAME TIME THE FO WAS CHKING WITH ZMA ON 127.47; I NOTICED THAT WE WOULD BE CLBING THROUGH THE ALT OF PASSING TFC. ZMA SAID THEY WERE LOOKING FOR ACR XY NOT XXY. AS I WAS ADJUSTING THE RANGE ON MY DISPLAY AND REALIZING THAT SOMETHING WAS OBVIOUSLY WRONG; WE GOT A TA; THEN AN RA. I HAD ALREADY DISCONNECTED THE AUTOPLT AND WAS LEVELING OFF. FREQ 127.47 TOLD US TO STOP OUR CLB AND THEN RETURNED US TO FREQ 125.07. WE CONFIRMED HE WANTED US AT FL290. SEVERAL MINS LATER WE WERE RETURNED ONCE AGAIN TO FREQ 127.47; BASICALLY WITHOUT FURTHER COMMENT. WE CAME WITHIN 300-500 FT VERTLY AND 1 1/2 - 3 MI HORIZLY OF OPPOSING TFC.