FLT CREW OF CL65 EXPERIENCE TCASII RA WHEN THEY WERE EITHER GIVEN OR MISHEARD A CLRNC TO DSND.

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WE WERE CRUISING AT FL310; THE CAPT TUNED RADIO #2 TO GET ARRIVING ATIS FOR DFW. I WAS HANDLING COM #1 AS PER COMPANY POLICY. ATC STARTED TO GIVE ME HOLDING CLRNC AND DSCNT ALT. IT CAUGHT ME OFF GUARD AND I READ BACK THE HOLDING CLRNC WHICH WAS 'ACR X; DSND AND MAINTAIN FL240 AND HOLD NE AT THE BIRLE INTXN AS PUBLISHED; EFC WILL BE XA25.' I READ BACK THE CLRNC AND QUESTIONED THE DSCNT ALT. ATC CONFIRMED TO DSND AND MAINTAIN FL240. AT THAT POINT I DIALED IN THE ALT GIVEN AND STARTED THE DSCNT TO FL240. THE AUTOPLT WAS ENGAGED DURING THIS ENTIRE TIME. MOMENTS LATER THE CAPT FINISHED COPYING ARRIVING ATIS AND I FILLED HIM IN ON ATC INSTRUCTION INCLUDING THE DSCNT TO FL240. THE CAPT PLUGGED IN THE PUBLISHED HOLD AT BIRLE AND SAID 'DO YOU LIKE THAT?' I QUICKLY LOOKED AT MY PFD AND MY ARR CHART AND SAID; 'YES; EXECUTE.' ON OUR WAY FROM FL260 WE RECEIVED A TCASII TFC ALERT. THE CAPT POINTED TO THIS ACFT AT ABOUT 10-11 O'CLOCK POS. I CONTINUED TO MONITOR MY DSCNT AND BEGAN A SPD REDUCTION FOR THE HOLD. JUST AT THAT MOMENT; WE RECEIVED AN RA TCASII ALERT 'TFC; TFC' WITH A CLB OR DSND (CANNOT REMEMBER AT THIS TIME). I TOOK THE AUTOPLT OFF AND SAID 'AUTOPLT DISENGAGED.' I COMPLIED WITH THE RA AND ADJUSTED PWR AS NEEDED. THE CAPT WAS CALLING OUT TCASII PROFILES. ATC THEN CAME BACK WITH 'ACR X; CLB TO FL250 OR FL260; TURN R TO HDG OF XXX; WHAT ALT WERE YOU ASSIGNED?' THE CAPT REPLIED 'ACR X; FL240; WE WERE RESPONDING TO A TCASII RA.' THE CTLR CAME BACK AND SAID WE WERE ASSIGNED FL270. THIS WAS THE FIRST TIME I HAD HEARD FL270. WE WERE GIVEN ADDITIONAL INSTRUCTION TO FLY AND RETURNED TO OUR ORIGINAL FLT PLAN. WE CONTINUED THE FLT WITH NO FURTHER INCIDENT.