AN ACR FK10 FLC HAS AN NMAC WITH A COMPANY SHORTLY AFTER TKOF IN IMC WX. THE FLC REACTED TO SEVERAL EXCITED COMMANDS FROM THE DEP CTLR AND FINALLY CLRED THE SIT BY FOLLOWING TCASII RA INSTRUCTIONS.

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TKOF CLRNC: AT 1500 FT TURN L 050 DEGS; CLB AND MAINTAIN 3000 FT. NORMAL TKOF. RWY HDG SWITCHED TO DEP. FREQ 124.10. CLBING THROUGH APPROX 1100 FT; I NOTICED TCASII TFC AT CLOSE PROX ABOVE 200 FT. AT 1500 FT I STARTED THE TURN TO 050 DEGS AND CALLED FOR HDG SELECTION. ATC CTLR (VOICE VERY EXCITED) INSTRUCTED COMPANY ACFT (ALSO ON THE FREQ) TO TURN IMMEDIATELY TO HDG 360 DEGS. ATC THEN INSTRUCTED US TO EXPEDITE TURN TO 360 DEG HDG WHILE CLBING. IN A VERY EXCITED VOICE; ATC INSTRUCTED US TO TURN R HDG 240 DEGS. I IMMEDIATELY REVERSED COURSE. I HEARD ON THE FREQ; 'I'M TURNING THEM. I'M TURNING THEM NOW!' AS I TURNED BACK TO THE 240 DEG HDG; TCASII RA CLB ALERT ANNOUNCED; FOLLOWED BY 'CLB; CLB NOW.' I RESPONDED IMMEDIATELY CLBING AT 3200 FPM TO CLR THE CONFLICT; WHILE THE CAPT ADVANCED THE THROTTLES TO EXPEDITE THE CLB. ONCE CLR OF TCASII CONFLICT; WE STABILIZED AT 4100 FT MSL ON 120 DEG HDG. THE CREW RESPONDED QUICKLY; DECISIVELY; WITH IMMEDIATE AND PROPER FLT CORRECTIONS TO ATC INSTRUCTIONS AS WELL AS TCASII RA ALERTS. WE WERE IFR THE ENTIRE DEP FROM 1000 FT AFL TO FL310 MSL AND WERE NOT ABLE TO DETERMINE HOW CLOSE WE WERE TO THE OTHER ACFT. TCASII ALERT INDICATED WITHIN 1 MI AND SAME ALT. AS WE EXPEDITED THE CLB; RED SQUARE DOUBLE 00 IN 12 O'CLOCK POS. ATC THEN CLRED US TO 8000 FT MAINTAIN HDG. WE REPLIED AND XMITTED WE HAD RESPONDED TO OUR TCASII RA.