FLC OF MLG STOPPED DSCNT AND CLBED IN RESPONSE TO A TCASII RA.

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IN CONTACT WITH LONG ISLAND APCH CTL; FOLLOWING RADAR VECTORS AT 11000 FT; WE WERE CLRED TO DSND TO 5000 FT. THIS SIT WAS MADE MORE DIFFICULT BECAUSE THE ACFT AUTO PRESSURIZATION CTLR HAD BEEN ON MEL SINCE JUN/XX/94. THE MANUAL CTLR WAS THE 'LOLLIPOP' TYPE. IT REQUIRES A LOT OF ATTN WITH EACH PWR CHANGE. AS I RETARDED THE THROTTLES; THE FO WAS INSIDE THE ACFT DEALING WITH THE PRESSURIZATION. WE NOTICED A TA AT OUR 12 O'CLOCK POS. THE FO QUESTIONED THE CTLR ABOUT THE TFC. BY THIS TIME; WE WERE ALREADY DSNDING THROUGH ABOUT 10000 FT. THE CTLR DID NOT RESPOND TO US. AT ABOUT 10000 FT; WE RECEIVED AN RA (MONITOR VERT DSCNT). AT THIS TIME; WE HAD APPROX 1500 FPM DSCNT. ACFT DSCNT WAS STOPPED AT APPROX 9700 FT THEN CLBED TO APPROX 10200 FT. AT THE BOTTOM OF THE DSCNT; BOTH THE FO AND MYSELF HAD VISUAL CONTACT WITH THE TFC (WHICH WAS 5 HIGH-PERFORMANCE S/E ACFT TRAILING SMOKE) IN FORMATION! WE QUESTIONED THE CTLR AGAIN ABOUT THE TFC; HE HESITATED; THEN SAID ONLY 'CONFIRM TFC IS AT 9000 FT.' THAT WAS THE ONLY MENTION OF THE TFC TO US BY ATC. WE NEVER DID FIND OUT WHY WE WERE CLRED TO DSND THROUGH THE TFC. MUST HAVE BEEN A SEVERE MIX-UP. TCASII SAVED US! WE RPTED THE EVENT TO THE CTLR AND HE NEVER SAID ANOTHER WORD ABOUT IT.