APCH CTLR CLRED CANADAIR CL65 FOR DSCNT TO A LOWER ALT AT PLT'S DISCRETION AND THEN INTERVENED SHORTLY AFTER THEY HAD STARTED THEIR DSCNT AND SENT THEM BACK TO THEIR PREVIOUS ALT THEY HAD JUST LEFT. CTLR ISSUED TA FOR A B737 CLBING AHEAD OF THEM TO AN ALT THROUGH WHICH THEY WERE GOING TO DSND.

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ATC TOLD US TO DSND AT PLT'S DISCRETION FROM 11000 FT TO 4000 FT. WE READ BACK THE CLRNC AND I SET 4000 FT IN THE ALT PRESELECTOR. THE CAPT ELECTED TO REMAIN AT 11000 FT SO WE COULD REMAIN AT CRUISE SPD (APPROX 320 KIAS) RATHER THAN HAVING TO SLOW TO 250 KIAS PASSING THROUGH 10000 FT. SOON THEREAFTER; ATC CALLED AND TOLD US TO 'DSND NOW' TO 3000 FT. WE READ BACK THE CLRNC AND 3000 FT WAS SET IN THE ALT PRESELECTOR. THE CAPT BROUGHT THE THRUST TO IDLE AND DEPLOYED SPD BRAKES TO BEGIN SLOWING TO 250 KIAS. HE THEN COMMANDED THE AUTOPLT TO BEGIN A NORMAL RATE OF DSCNT. PASSING 10500 FT; ATC CALLED TO AMEND OUR ALT AND TOLD US TO CLB BACK UP TO 11000 FT. IN THE SAME BREATH; ATC CALLED B737 TFC AT OUR 11 O'CLOCK; CLBING TO 10000 FT AND APPROX 5 MI. I IMMEDIATELY READ BACK THE CLRNC AND SET 11000 FT IN THE ALT PRESELECTOR WHILE THE CAPT DISENGAGED THE AUTOPLT AND PITCHED UP. HE THEN ADDED THRUST AND RETRACTED THE SPD BRAKES WHILE THE AIRPLANE TRANSITIONED TO A CLB. TCASII THEN ISSUED A TA AND WHEN WE BROUGHT UP THE DISPLAY THE YELLOW CIRCLE WAS AT 11 O'CLOCK AND APPROX 3 MI STILL IN A CLB. THE CAPT ACQUIRED THE TARGET VISUALLY AND WE NOTIFIED ATC. BUT THE CAPT ALSO STOPPED CLBING AT APPROX 10700 FT EVEN THOUGH THE FLT DIRECTOR SHOWED A CLB COMMAND TOWARD 11000 FT. I TOLD HIM THAT WE NEEDED TO CONTINUE THE CLB TO 11000 FT; BUT THERE WAS NO RESPONSE. BY THIS TIME THE TFC REACHED ITS CLOSEST POINT OF 700 FT BELOW AND 1.5 MI FROM OUR ACFT. I AGAIN SAID TO THE CAPT THAT WE HAD BEEN ASSIGNED 11000 FT AND ASKED WHY HE WAS NOT CLBING. ATC HAD SAID TO MAINTAIN VISUAL WITH THE TFC AND DSND WHEN PASSING CLR. THE CAPT AT THIS POINT; AND AT APPROX 10700 FT; ASKED ATC IF WE COULD CONTINUE OUR DSCNT. ATC SAID WE WOULD CONTINUE OUR DSCNT. THE ALT PRESELECTOR WAS RESET ACCORDINGLY AND DSCNT WAS INITIATED.