B737 FLC INITIATE EVASIVE TCASII RA CLB IN CONJUNCTION WITH D10 CLB CLRNC DUE TO CONFLICTING TFC AT SAME ALT.

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WE WERE FLYING A DEP FROM DAL TO TUL. WE HAD BEEN AT AN INTERMEDIATE LEVELOFF OF 17000 FT FOR SEVERAL MINS. WE HAD A TA AND ACQUIRED ON TCASII A TARGET AT 16500 FT OFF THE NOSE. ALMOST SIMULTANEOUSLY WE GOT A CALL FROM REGIONAL DEP (I THINK; ALTHOUGH WE MAY HAVE BEEN WITH ZFW) TO FIRST TURN 10 DEGS R AND START A DSCNT. THEN ALMOST IMMEDIATELY WE GOT A CLB RA. THEN ALMOST SIMULTANEOUSLY THE CTLR SAID MAINTAIN 340 DEG HDG (WHICH WE HAD BEEN ON FOR SEVERAL MINS) AND CLB TO FL180. WE COMPLIED AND AS I WAS LOOKING FOR THE TARGET I KNEW TO BE AT 16500 FT; I SAW A FOKKER JET AT ABOUT MY 7-8 O'CLOCK POS AT ABOUT THE SAME ALT. HE MAY HAVE TAKEN SOME EVASIVE ACTION. I HEARD HIM LATER SAY ON THE RADIO THAT HE HAD GOTTEN A DSND RA FROM 17000 FT WHICH WAS ALSO HIS ASSIGNED ALT. HE STATED THAT 'HE DIDN'T WANT TO FOLLOW THE RA BECAUSE OF THE LIGHT ACFT AT 16500 FT.' IT WAS A PRETTY TENSE MOMENT FOR BOTH ACR'S. I DON'T KNOW IF THE SMALL ACFT WAS ON ANY FREQ; WE NEVER HEARD HIM. I HESITATE TO SAY WE TOOK EVASIVE ACTION BECAUSE OUR CLB FROM THE CTLR WAS ALMOST COINCIDENTAL WITH THE RA. I ESTIMATE THE DISTANCE WHEN I SAW THE JET TO BE ABOUT 15 MI.