AN ATX GULFSTREAM IV CREW HAD TO TAKE EVASIVE ACTION NO TURN ON SID TO AVOID CLOSING ON AN INTRUDER ACFT RIGHT AFTER TKOF. WX FACTORS 100 FT CEILING WITH 400 FT TOPS.

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I BELIEVE THE PROB WAS THE TRANSITION OF PREVIOUS ACFT DEPARTING ON SAME RWY BEING VECTORED THROUGH A SID WHICH WAS TO BE USED BY OUR ACFT. I ALSO BELIEVE THAT A FREQ HDOF FROM THE TWR CTLR TO DEP CTL MAY HAVE CONTRIBUTED TO COM BREAKDOWN BTWN OUR ACFT AND ATC. THE DIFFERENCE IN OUR COURSE ON DEP AND THE COURSE REQUIRED ON THE SID WAS ONLY 20 DEG DIFFERENCE (THE SID REQUIRED A TURN OUT OF 400 FT TO A HDG OF 300 DEGS WHEREAS THE ACFT WAS FLOWN ON A 320 DEG HDG BECAUSE OF TCASII ALERT). HIGH PERFORMANCE ACFT IN VERY LOW VISIBILITY SITS SHOULD BE KEPT WELL APART AND NO TURN ON COURSE SHOULD BE APPROVED UNTIL ALL ACFT ARE WELL AWAY FROM THE DEP AREA. I BELIEVE THAT PERHAPS THE TWR CTLR SHOULD BE INSTRUCTED TO STAY WITH A DEPARTING ACFT (ASSUMING RADAR COVERAGE) UNTIL HE HAS SAFELY MADE A TRANSITION TO A DEP SEGMENT. AS THE GULFSTREAM IN FRONT OF US WAS CLRED FOR TKOF ON RWY 32; WE WERE TOLD TO TAXI INTO POS AND HOLD. SOON AFTER WE WERE CLRED FOR TKOF. ALL OPS ON TKOF PROCEEDED NORMALLY WITH THE TCASII SET ON AND THE TFC ALERT AND RA MODES SET ON. AFTER ROTATION OF THE ACFT AND CLB THROUGH THE LOW FOG BANK INTO CLR WX (APPROX 300-400 FT AGL); A YELLOW THEN RED TCASII ALERT WAS ACTIVATED WITH THE TARGET CONVERGING FROM THE L OF THE ACFT. THE ACFT WAS IN FULL SIGHT OF THE CREW AND THE CAPT ELECTED NOT TO COMMENCE THE L HAND TURN TO 300 DEGS AS PUBLISHED FOR FEAR OF A COLLISION. CONCURRENT WITH THIS EVENT WAS A FREQ HDOF FROM THE TWR CTLR TO DEP CTL WHICH CONTRIBUTED TO THE WORKLOAD. AS THE FREQ WAS CHANGED; THE DEP CTLR ISSUED INSTRUCTIONS TO IMMEDIATELY STOP OUR CLB AS WE CHKED IN ON FREQ. THE CAPT ELECTED TO MONITOR THE CONVERGING TFC VISUALLY AND PROCEED IN A MANNER THAT WOULD KEEP BOTH ACFT SAFELY SEPARATED. LATERAL SEPARATION BTWN THE GULFSTREAM THAT DEPARTED IN FRONT OF OUR ACFT APPEARED TO BE ADEQUATE; APPROX 3-5 MI. THIS DID NOT APPEAR TO BE THE ACFT THAT CAUSED THE ALERT. THE ACFT THAT WAS XING L TO R IN FRONT OF US WAS CLBING THROUGH OUR ALT AND IS ESTIMATED TO BE APPROX 1/2 TO 1 MI IN FRONT OF OUR ACFT. AFTER VISUAL SEPARATION HAD BEEN ESTABLISHED; THE CAPT ELECTED TO FLY A HEADING THAT WOULD PROVIDE SAFE SEPARATION. NO FURTHER INFO REGARDING THIS EVENT WAS RELAYED TO OUR ACFT BY DEP CTL.