FLC OF B727 ON DEP CLB HAVE 2 ACFT ON TCASII; ONE ABOVE AND ONE BELOW. WHEN THEY QUERY ATC THEY ARE GIVEN AN IMMEDIATE; BEST RATE CLB INSTRUCTION. INITIATING THE CLB THEY RECEIVE A TCASII RA TO MONITOR VERT SPD. THE CLB IS STOPPED. DEP CTLR THEN GIVES A VECTOR TO TURN.

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WE DEPARTED RWY 18L IN MEM WITH AN ASSIGNED HEADING L TO 60 DEGS AND MAINTAIN 5000 FT. THIS HEADING TOOK US THROUGH AN ARR CORRIDOR FOR RWY 18L. DEP FAILED TO ISSUE US A CONTINUED CLB CLRNC. WE OBSERVED 2 TCASII TARGETS WITH A 'TFC' ALERT FROM TCASII. WE ASKED DEP IF THEY WANTED US TO CLB AND INFORMED THEM OF OUR TFC CONFLICT. HE RESPONDED 'CLB NOW BEST RATE.' HE DID NOT GIVE US AN ALT TO CLB TO. WE IMMEDIATELY INITIATED A CLB BUT AT THAT SAME MOMENT; PASSING 5100 FT; WE RECEIVED A TCASII RA OF 'MONITOR VERT SPD.' SO WE STOPPED CLB AT 5100 FT. ONE TARGET ACFT WAS INDICATING 300 FT ABOVE AND ONE 100 FT BELOW. BOTH WERE RED ON TCASII. THEN DEP SAID 'TURN L TO 350 DEGS.' WE STARTED THE TURN THEN RECEIVED 'CLR OF CONFLICT.' AS WE STARTED THE L TURN BOTH ACFT PASSED US; ONE UNDER; ONE OVER; BUT OFFSET HORIZLY AT LEAST 1/4 MI. WE; THE PLTS; NEVER SAW THE OTHER ACFT; HOWEVER; MEM DEP HAD THEM ON THEIR RADAR. ON THE TCASII DISPLAY BOTH TARGETS PASSED VERY CLOSE TO OUR ACFT POS SYMBOL. AFTER THEY PASSED AND AFTER 'CLR OF CONFLICT;' DEP; HAVING SEEN WHAT OCCURRED; AGAIN CLRED US TO 'CLB BEST RATE TO 13000 FT.' WE INFORMED THEM THAT WE HAD AN RA; WHICH WE FOLLOWED. I THINK THERE MAY HAVE BEEN CTLR TRAINING TAKING PLACE. 2 DIFFERENT VOICES WERE HEARD THROUGH THIS EPISODE. THE TCASII PROBABLY SAVED A POSSIBLE COLLISION. THE RADAR TAPES MAY SHOW THE ACTUAL PROX OF THE CONFLICT ACFT. THE KEY IS VIGILANCE IN A BUSY ATA TO MINIMIZE THE RISK OF A CONFLICT; HOWEVER; UNDER POSITIVE CTL WE PUT OUR FAITH AND LIVES IN THE HANDS OF THE CTLR.