ACR Y TOOK ACR X CLRNC; HAD LTSS WITH ANOTHER ACFT.

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I WAS WORKING R19 AT ZDC DURING A PERIOD OF MODERATE TFC AND WX DEVS. SEVERAL ACFT ON NANCI 5 (LGA) ARR NEEDED TO DEVIATE NEAR DQO VOR. I ISSUED DSCNT TO 2 ACFT TO 11000 FT AND ADVISED ACR X TO DEVIATE E OF COURSE AFTER LEAVING 16000 FT. AFTER UNKEYING MIKE; THERE WAS SOME GARBLE ON FREQ AND THEN ACR X COMPLETED READBACK OF ALT CLRNC. SEVERAL SECONDS LATER I OBSERVED ACR Y DSND BELOW FL240 AND CROSS WITH TFC BELOW AT FL230. I ASKED Y TO VERIFY ASSIGNED ALT AS FL240 AND CREW RESPONDED I HAD GIVEN DSCNT TO 11000 FT. I WAS NOT AWARE THAT Y WAS ON MY FREQ AND ATTRIBUTED GARBLED NOISE TO Y CHKING ON AT FL240. THE ACFT MISSED BY 4 PLUS MI AND WERE ALREADY MOVING AWAY FROM EACH OTHER; SO THERE WAS NO FURTHER NEED FOR ACTION ON MY PART. THE Y CREW MUST HAVE THOUGHT THE CLRNC FOR X WAS THEIRS. I GUESS I COULD HAVE RESPONDED TO THE GARBLE TO VERIFY NO ONE ELSE TOOK CLRNC; BUT THERE WAS REALLY NO NEED IN MY MIND TO VERIFY SINCE Y WAS NOT ON THE FREQ AS FAR AS I KNEW. REVIEW OF TAPES SHOWED Y WAS ON WHEN I ASSUMED POS. MY FAILURE TO RECOGNIZE A POTENTIAL CONFLICT WITH ACFT ACCEPTING A CLRNC AND THE CREW'S PART OF NOT LISTENING TO CALL SIGNS LED TO THIS OCCURRENCE. SUPPLEMENTAL INFO FROM ACN 312940: FO FLYING THE WARRD 4 ARR TO EWR AT FL240 AT RIDGY. RECEIVED CLRNC TO DSND TO 11000 FT BY ZDC. APCH HAS AN EXPECT CLRNC TO CROSS HOLEY AT 11000 FT. STARTED DSCNT UPON RECEIVING CLRNC. AT ABOUT FL220; ZDC REQUESTED OUR CLRNC LIMIT; WE TOLD THEM 11000 FT. THEY SAID TO STOP AT 16000 FT. AFTER CHANGING CTLING FREQ; WE WERE ASKED TO CONTACT ZDC ON THE GND. WE COULD HAVE ACCEPTED ANOTHER FLT'S CLRNC AND OUR READBACK WAS POSSIBLY COVERED. WE HAD TCASII SET AT 40 DME AND BELOW AND HAD NO TARGETS. ON THE GND ATC SAID WE HAD APCHED ANOTHER ACFT BY 400 FT VERTLY AND 4.3 MI HORIZLY.