FLC OF A B737-300 DSNDED AND TURNED DURING INITIAL CLBOUT IN RESPONSE TO TCASII RA CAUSED BY ANOTHER ACFT DSNDING CONTRARY TO THEIR CLASS C CLRNC.

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ON INITIAL CLBOUT ON PWM 4 DEP CLRED US TO 3000 FT RWY HDG OFF RWY 29 AT APPROX 2900 FT. TA SOUNDED; THEN IMMEDIATELY FOLLOWED BY RA TO 'DSND.' VSI INDICATED 3000-3500 FPM DSCNT AND RA SOUNDED 'DSND; DSND NOW.' FO WAS PF AND HESITATED. I TOOK OVER CTLS; STARTING DSCNT AND A L TURN TO APPROX 240 DEG HDG. AT APPROX 2200 FT; TCASII ADVISED 'CLR OF CONFLICT.' WE ADVISED ATC OF TCASII RA/ALTDEV. WE WERE THEN CLRED TO 10000 FT ON HDG OF 240 DEGS. NEXT XMISSION HEARD WAS FROM ATC TO OTHER ACFT STATING 'NOT TOO BRIGHT TO DSND INTO TFC.' TFC WAS NEVER SEEN. WE WERE GIVEN ON; INITIAL CLB; A TA AND WERE LOOKING. I WAS PNF; PERFORMED MY DUTIES; CALLED TO FO WHO HAD PF TFC AHEAD. AS HE STARTED LEVELOFF; TFC HAD STATED SOMEWHERE I THINK HE HAD US IN SIGHT. WE NEVER SAW HIM. AT FIRST TA; FO/PF WAS LEVELING AT 3000 FT WHEN RA SOUNDED FOR DSCNT HE HESITATED. TCASII SHOWED RED BOX RIGHT ON TOP OF US. 'DSND; DSND NOW' WAS HEARD AS I WAS TAKING OVER CTLS. TURN HAD OR WAS GIVEN TO US AT THIS TIME TO TURN TO HDG 240 DEGS. IMMEDIATE TURN AND DSCNT WAS INITIATED AND WAS STOPPED APPROX 2200-2000 FT WITH 'CLR OF CONFLICT' ANNOUNCED. FO WAS GIVEN ACFT BACK TO ASSUME PF DUTIES FOR REMAINDER OF FLT.