TCASII ALERTS AN ACR CREW TO A POSSIBLE CONFLICT.

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DURING CLB WITH DEP CTL AT APPROX 2000-3000 FT; WE WERE TOLD TO LEVEL AT 5000 FT; TO EXPECT FURTHER CLB ONCE PAST TFC. THERE WERE LAYERED CLOUDS BEGINNING AT 7500 FT; BUT WE WERE IN CLR AIR UNTIL REACHING THE HIGHER CLOUD LAYER. WE ASKED THE CTLR IF OUR TFC WAS AT 1-2 O'CLOCK. HE HESITATED; BUT EVENTUALLY CONFIRMED THAT AREA. AT 3000 FT WE RPTED THAT WE HAD VISUAL CONTACT AND A TCASII RETURN THERE; AND IF HE AGREED; WE WOULD CONTINUE CLB. THE CTLR SAID TO MAINTAIN OUR OWN CLRNC AND CLB TO 15000 FT. GOING THROUGH 5000 FT WE OBSERVED THAT WHAT WE BELIEVED OUR TFC TO BE WAS NO LONGER A POTENTIAL CONFLICT. THE TCASII SCREEN IN THE COCKPIT SHOWED NO TFC IN FRONT OF US ON THE 20 MI SCOPE SELECTION. I WAS LOOKING FOR AN AIRWAYS MAP WHEN; AT ABOUT 7000 FT; THE COPLT SAW AN ACFT RETURN ON THE TCASII SCREEN AT A RANGE OF AROUND 6 MI. WE IMMEDIATELY GOT AN AMBER CAUTION ALERT. I TOOK MANUAL CTL OF THE ACFT; AND IMMEDIATELY A RED ALERT ADVISORY OCCURRED. REALIZING THAT THE ACFT THAT APPEARED ON THE SCREEN WAS ABOVE OUR ALT. I BEGAN TO LEVEL THE ACFT; AND BANKED THE ACFT TO AVOID NEGATIVE G'S. THE DEP CTLR SAID THAT HE HAD RETURNS MERGING. I REPLIED THAT WE HAD LEVELED OFF BELOW THE OTHER ACFT. AUTOTHROTTLES WERE ENGAGED AND A SELECTED AIRSPD OF 250 KTS. HOWEVER; THE THROTTLES DID NOT RETARD SO AIRSPD MOMENTARILY INCREASED TO 310 KTS. ONCE CLR OF THE OTHER ACFT; WE RESUMED CLB. RPT WAS FILED UPON RETURN TO IAH THAT EVENING; AND A CALL TO OUR SYS CTL WAS MADE. THEY INDICATED THAT NO INQUIRIES WERE MADE BY DEP CTL (ATC) OR TCASII ACTION BY ANOTHER ACFT RECEIVED. OBVIOUSLY; IF THE CONFLICTING TFC WAS OUR ORIGINAL TFC AND NOT ANOTHER POP-UP ACFT; WE MISIDENTED THE TFC TO STAY CLR OF. ALSO; IT IS NOT A GOOD IDEA TO ATTEMPT A CLB WHEN THERE ARE HIGHER CLOUD LAYERS; EVEN THOUGH WE WERE IN VFR CONDITIONS WHEN WE FELT WE HAD CONTACT WITH THE ACFT AFFECTING OUR CLB. THE ORIGINAL TFC WE IDENTED WE FELT WAS AT 6000 FT (WHICH IS NORMAL IN THAT AREA); SO WHEN WE PASSED THAT ALT; WE FELT THE CONFLICT WAS RESOLVED. I DO NOT RECALL ASKING OR BEING GIVEN THE ALT OF THE CONFLICTING TFC WHEN WE ORIGINALLY IDENTED IT AT 1-2 O'CLOCK. MISCOM ALSO PLAYED A PART IN THE PROB.