CAPT OF A B737 DIRECTED THE PF TO LEVEL OFF TO AVOID A TWIN ENG ACFT HE HAD SIGHTED OUT THE PF FO'S WINDOW. A TCASII RA THEN WARNED TO DSND CAUSING ACFT TO PASS WITHIN 500-1000 FT OF EACH OTHER.

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WE REQUESTED AND WERE TOLD TO TAXI TO RWY 26. WE REQUESTED RWY 21 (SURFACE WINDS WERE SUITABLE FOR EITHER RWY); AND GND INSTRUCTED US TO TAXI TO RWY 21. DURING TAXI OUT; GND AMENDED OUR INITIAL ALT FROM 10000 FT TO 7000 FT. TWR CLRED US TO TAKE OFF; INSTRUCTING US TO MAINTAIN RWY HDG. AFTER TKOF (FO FLYING); WE FOLLOWED NORMAL CLEAN-UP PROCS. IMMEDIATELY AFTER COMPLETING FLAP RETRACTION; TWR CALLED OUT TFC TO OUR R AT 7000 FT. I LOOKED OUT THE FO'S SIDE WINDOW (R2) AND PICKED UP THE TFC. I FIRST DIRECTED THE FO TO LEVEL OFF; THEN QUICKLY DIRECTED HIM TO START A DSCNT; WHICH HE DID. VERY QUICKLY AFTER STARTING THE EVASIVE MANEUVER; THE TCASII GENERATED AN RA ('DSND'); WHICH WE HAD ESSENTIALLY ALREADY STARTED; AND WE COMPLIED WITH THE RA GUIDANCE. AS WE STARTED THE DSCNT; I LOST SIGHT OF THE TFC ABOVE AND BEHIND OUR ACFT; THEN REGAINED SIGHT OUT TO THE L SIDE OF THE ACFT. I DO NOT KNOW IF THE OTHER ACFT TOOK ANY EVASIVE ACTION -- NO RADIOS CALLS WERE MADE BY THE OTHER ACFT TO THAT EFFECT. IMMEDIATELY AFTER THIS; TWR DIRECTED US TO CONTACT DEP. WHEN I CHKED IN WITH DEP; I ASKED DEP TO CONFIRM THAT THE TWIN WAS AT 7000 FT (WITH THE IMPLIED QUESTION OF 'WHY?'). DEP SAID SOMETHING INDICATING THERE HAD BEEN A MIX-UP BTWN TWR AND DEP ('WE THOUGHT YOU WERE TAKING OFF ON RWY 26'). POINT OF MINIMUM SEPARATION OCCURRED ABOVE AND BEHIND OUR ACFT AND OUT OF MY SIGHT. I DON'T BELIEVE WE WERE EVER WITHIN 500 FT OF EACH OTHER; SO I WOULDN'T CLASSIFY THIS AS A NMAC. HOWEVER; WITH THE CAVEAT THAT MY PERCEPTIONS ARE PROBABLY AFFECTED BY THE HEAT OF THE MOMENT; I WOULD ESTIMATE THE MINIMUM ALT SEPARATION AT ABOUT 500 FT AND MINIMUM HORIZ SEPARATION AT 1000 FT; WITH ABOUT A 30 DEG HDG XING ANGLE. IN ADDITION; OUR MINIMUM SEPARATION WOULD LIKELY HAVE BEEN LESS WITHOUT THE EVASIVE ACTION TAKEN. BECAUSE OF THE TCASII'S 1200 FT CLBING INHIBIT POINT FOR RA'S; THE TCASII RA WAS PROBABLY DELAYED IN THIS SIT. AS A RESULT; I'M NOT SURE HOW EFFECTIVE THE RA WOULD HAVE BEEN IN THIS SIT IF WE HAD NOT ALREADY STARTED THE EVASIVE MANEUVER. WHILE THIS SIT IS OBVIOUSLY SOMEWHAT UNIQUE; WE MAY WANT TO RE-EVALUATE THE WAY THE TCASII IS PROGRAMMED TO HANDLE THESE KINDS OF SITS.