CL65 FLT CREW REPORTS TCAS RA WITH UNKNOWN ACFT AT FL330; 80 NW OF GQO.

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AT FL330 APPROX 80 MI NW OF GQO HDG ABOUT 150 DEGS IN IMC; WE WERE CLRED TO FL240. ATC ADVISED US OF A TARGET AT 10-11 O'CLOCK POS NWBOUND AT 1500 FT BELOW US. HE SAID IT WAS PROBABLY AN ERRONEOUS TARGET. WE INITIALLY STARTED TO DSND BUT IT APPEARED TO US TO BE A REAL TARGET AND IT WAS CLBING. WE STOPPED THE DSCNT AT FL327 TO BE SURE THERE WOULD BE NO PROB. WE THEN RECEIVED A TA AND (I THINK) ADVISED ATC. WE THEN RECEIVED AN RA WITH CLB INSTRUCTIONS OF 2100 FPM. WE IMMEDIATELY COMPLIED WITH THE RA AND ADVISED ATC. THE OTHER TARGET CONTINUED TO CLB AND LEVELED AT FL330 BELOW US. WHEN WE RECEIVED THE 'CLR OF CONFLICT' MESSAGE FROM TCAS WE WERE AT ABOUT FL337. WE THEN TOLD ATC WE WERE CLR OF THE TARGET AND CONTINUING OUR DSCNT TO FL240. ATC NEVER MADE ANOTHER MENTION OF THE INCIDENT AND THINGS HAPPENED SO QUICKLY; AND WE WERE SO FIXED ON THE INCIDENT AND CONTINUING TO ZZZ THAT WE NEVER HAD A CHANCE TO INQUIRE ABOUT THE INCIDENT WITH ATC. I FEEL THIS TARGET WAS AN ACTUAL ACFT THAT ATC DIDN'T KNOW ABOUT AND IF WE HAD CONTINUED THE DSCNT THE RESULTS COULD HAVE BEEN AN INCURSION OR WORSE.