MLG HAS TCASII RA FOR TFC OPPOSITE DIRECTION SAME ALT.

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WE WERE CRUISING AT FL250 AND WORKING WITH ZDC ON FREQ 134.62 ENRTE RDU-PIT. WASHINGTON WAS APPARENTLY LATE IN HANDING US OFF TO WASHINGTON ON 133.02. AS WE SWITCHED OVER TO 133.02 WE HEARD THE CTLR ASKING US IF WE WERE ON THE FREQ. WE RESPONDED 'YES; THEY JUST SWITCHED US OVER AND WE ARE CHKING IN AT FL250.' HE RESPONDED; 'ROGER;' AND NOTHING MORE. AFTER 5 MINS OR SO; RECEIVED A 'TFC' WARNING ON THE TCASII. AFTER CHKING TCASII WE NOTICED; 11 O'CLOCK CONVERGING TFC AT OUR SAME ALT. STILL NO RESPONSE FROM ATC. INSIDE OF 10 MI; RECEIVED AN RA WARNING ON TCASII FOLLOWED SHORTLY BY A 'DSND' COMMAND. AT ABOUT THE SAME TIME; ZDC ASKED US IF WE WERE AT FL240 -- WE RESPONDED 'NEGATIVE;' LEVEL AT FL250 ASSIGNED.' WE CONTINUED INITIATING A 2500-3000 FPM DSCNT TO FL240 AS ATC THEN STARTED ISSUING CLB INSTRUCTIONS TO THE CONVERGING TFC AND DSND INSTRUCTIONS TO US. HE WAS TALKING SO FAST HE COULD HARDLY SPIT THE WORDS OUT! AS WE LEVELED AT FL240; WE THEN SAW THE TFC PASS OVERHEAD. THE WHOLE EVENT TOOK 15-20 SECONDS -- NO MORE. I THEN REQUESTED AN EXPLANATION FROM ATC -- WHO SAID THAT HE ISSUED US A CLRNC TO FL240; AND THAT A COMPANY ACFT MUST HAVE ANSWERED FOR US. WE RESPONDED THAT WE CHKED IN AT FL250; AND NEVER RECEIVED A CLRNC TO FL240; NOR DID WE EVER RESPOND TO ANY SUCH CLRNC. HE THEN RESPONDED; 'ROGER; HIS MISTAKE.' HE THEN SWITCHED US TO ANOTHER FREQ. HAD IT NOT BEEN FOR TCASII THIS COULD HAVE EVOLVED INTO A VERY SERIOUS SIT. IT ALERTED US TO THE POTENTIALLY DANGEROUS TFC.