FLC OF AN MLG STOPPED CLB TO DSND IN RESPONSE TO A TCASII RA.

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OVER LOUISVILLE (IIU) WE WERE CLRED DIRECT TO POCKET CITY (PXV) AND WERE CLBING THROUGH APPROX 25500 FT TO A CLRED FL260. OUR VNAV HAD BEGUN TO CAPTURE AT ABOUT 25000 FT. WE RECEIVED A TCASII ALERT FOLLOWED WITHIN A FEW SECONDS BY AN RA COMMANDING A 4000 FPM DSCNT. THE RED TFC INDICATOR ON THE TCASII SCREEN INDICATED TFC AT 12 O'CLOCK LEVEL AT FL270. THE FO (PF) FOLLOWED THE COMMANDED DSCNT PER (ACR X) DIRECTIVES; AND DSCNT WAS ACCOMPLISHED TO ABOUT 24500 FT. WE IMMEDIATELY ADVISED ZID OF OUR TCASII COMMANDED DSCNT AND QUERIED HIM ABOUT THE UNANNOUNCED TFC. HIS RESPONSE WAS SIMPLY THAT 'YES; THERE WAS TFC (OPPOSING) AT FL270; AND HE REQUESTED US TO CLB BACK THROUGH FL250 (FOR FL260) ASAP. WE WERE ALREADY DOING SO AND LEVELED SHORTLY AT FL260. THIS TCASII RA MAY HAVE BEEN BROUGHT ABOUT BY THE COMPUTER ASSUMPTION OF OUR CLB RATE (VNAV HAD BEGUN TO CAPTURE ABOUT 1000 FT BELOW 26000 FT (ASSIGNED). HOWEVER; THERE WERE SEVERAL TARGETS ON THE TCASII SCREEN; THE CTLR WAS BUSY AT THE TIME AND HAD GIVEN US NO NOTIFICATION OF OPPOSING TFC. NEEDLESS TO SAY; THE EVENT WAS VERY UNSETTLING; AND POINTS OUT THE PROBS YET TO BE CORRECTED IN THE TCASII SYS.