A CLBING DC9 CREW SAW AND AVOIDED; VISUALLY; ANOTHER ACFT THAT WAS IN CONFLICT WITHIN CLASS A AIRSPACE. TCASII TA HAD ALERTED THE CREW. CTLR HAD JUST ISSUED A REQUEST FOR A TURN AND AN INCREASED CLB. THAT AMENDED CLRNC WAS IN CONFLICT WITH THE FOLLOWING TCASII RA ISSUED FOR A DSCNT.

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HAD BEEN GIVEN A VECTOR TO CRL WHILE NE OF PECK; AND HAD SWITCHED OVER TO THE CRL VOR; BUT NOT RECEIVING YET. SAW OTHER ACFT ON TCASII DISPLAY SHORTLY AFTER IT CAME ON 14 NM SCALE. IT WAS ABOVE US AT; I THINK; 1200 FT AND IT LOOKED LIKE A POSSIBLE CONFLICT. MY INSTINCT WAS TO INCREASE THE RATE OF CLB. THERE WAS A KNOCK ON THE COCKPIT DOOR BY THE FLT ATTENDANT; A 'TFC' ALERT FROM THE TCASII; NOT EXACTLY CERTAIN OF EXACT ORDER OF THOSE EVENTS. JUST PRIOR TO THAT; THE CTLR HAD ISSUED A 20 DEG TURN TO THE L AND A REQUEST FOR AN INCREASE IN CLB RATE (SECONDS BEFORE). I HAD ALREADY STARTED TO INCREASE THE RATE OF CLB; AND AT HIS REQUEST I INCREASED THE RATE EVEN MORE. ALL THIS TIME I HAD THE OTHER ACFT IN SIGHT. I THOUGHT THAT THE SUDDEN INCREASE IN THE RATE OF CLB TRIGGERED THE TCASII TO COMMAND A DSCNT; BUT BY THEN THE RATE OF CLB WAS GREAT; AND I COULD SEE THAT THE BEARING TO THE OTHER ACFT WAS DRIFTING TO THE R; AND HE WAS IN A L TURN. THE TCASII WAS COMMANDING FULL RATE DOWN; AND TO DO THAT WOULD HAVE REQUIRED NEGATIVE G'S; AND RATHER THAN INJURE OR KILL SOMEONE IN THE REAR OF THE ACFT; I CONTINUED IN A SLIGHT L TURN SO AS NOT TO LOSE SIGHT OF THE OTHER ACFT; AND LEVELED OFF WITHOUT PULLING NEGATIVE G'S. THE OTHER ACFT PASSED DOWN OUR R SIDE ABOUT 500 FT ABOVE US AND ABOUT 3 MI ABEAM (ESTIMATED).