AN ACR MLG HAD A TCASII ALERT TO DSND WHILE TRYING IN VAIN TO MAINTAIN VISUAL CONTACT WITH THE ACFT AHEAD THAT HAD JUST MADE A GAR.

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AN ACFT WAS EXECUTING A GAR ON THE PARALLEL RWY AT DFW. THE TWR ASKED US TO MAINTAIN VISUAL CONTACT. JUST BEFORE THIS; MY COPLT HAD POINTED OUT THE TFC AND HAD STATED THAT WE SHOULD KEEP AN EYE ON HIM. WE SWITCHED TO DEP CTL AND THEY ASKED IF WE HAD THE TFC IN SIGHT. THE ACFT WAS ABOUT 5 MI AHEAD AND CLBING OUT. THE WX WAS PARTLY CLOUDY -- SCATTERED CLOUDS. KEEPING THE TFC IN SIGHT WAS NOT A PROBLEM. DEP ISSUED OUR TFC; WHICH WAS AHEAD OF US IN A TURN TO THE R. THEY THEN GAVE US A R TURN AS WELL. IT WAS A 90 DEG TURN AND WE WERE CLBING THROUGH ABOUT 3000 FT ON A CLRNC LIMIT OF 10000 FT. AS THE COPLT WAS MAKING THE TURN; I REALIZED THAT WE WERE NOT GOING TO BE ABLE TO MAINTAIN VISUAL CONTACT WITH OUR TFC. I WAS INFORMING DEP CTL THAT OUR TFC WAS ABOUT TO BE LOST WHEN WE RECEIVED A TA ON OUR TCASII FOLLOWED BY AN RA 'DSND' COMMAND. I LOOKED AT OUR ALT WHICH WAS ABOUT 4500 FT AND THE ALT OF THE BLIP ON THE TCASII SCREEN SHOWED A PLUS/MINUS 600 FT. I WAS ALSO AWARE THAT WE WERE STILL CLBING AND SO I ASSISTED THE COPLT IN BEGINNING A DSCNT BY PUSHING THE YOKE DOWN AND TELLING HIM TO GET IT DOWN AND FOLLOW THE RA. AT THE SAME TIME; DEP CTL RESPONDED TO MY CALL AND TOLD US TO DSND TO 4000 FT AND MAINTAIN VFR. IT WAS ALL VERY BUSY AND QUICK. I THOUGHT I COULD MAINTAIN VISUAL CONTACT; BUT THE 90 DEG TURNS QUICKLY CHANGED THE PICTURE. I DON'T UNDERSTAND WHY DEP ISSUED A CLRNC THAT WOULD BE IN CONFLICT; VISUAL OR OTHERWISE. THERE WAS NO WAY THAT WE COULD HAVE AVOIDED THE EVASIVE TCASII MANEUVER. I THINK NOW IT WILL BE VERY DIFFICULT FOR ME TO ACCEPT ANY VISUAL SEPARATION CLRNC.