FLC OF A CPR FALCON 20F DID NOT RESPOND TO A TCASII RA DURING VECTORS TO THE ILS SINCE APCH CTLR HAD PROVIDED A TA; DSCNT LEVELOFF AND TURN TO ASSURE TFC SEPARATION. IN ADDITION; THE FLC HAD THE B737 SIGHTED.

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WE WERE EBOUND ON A R DOWNWIND LEG; VECTORS FOR THE ILS TO RWY 26R AT ATL; AND DSNDING TO 5000 FT AS ASSIGNED BY ATC. OUT OF APPROX 6500 FT; THE TCASII ISSUED A TA FOR TFC AT OUR 9:30 O'CLOCK POS. WE ESTABLISHED VISUAL CONTACT WITH ACFT Y PAX JET AT APPROX 2 1/2 MI AND 400 FT BELOW US. I BELIEVE IT WAS A B737. WE STOPPED THE DSCNT. AT THE SAME TIME; ATL APCH ORDERED US TO LEVEL AT 6000 FT AND TURN R TO A HDG OF 130 DEGS. UPON LEVELING AT 6000 FT; THE TCASII ISSUED A 'CLB' RA. SINCE WE HAD VISUAL CONTACT WITH THE OTHER ACFT; AND IT WAS CLR THEY WOULD DSND BELOW US; WE MAINTAINED 6000 FT. ACFT Y WAS ON A HDG OF APPROX 180 DEGS. THEY WERE ALSO DSNDING. THE TCASII WAS THE FIRST WARNING OF AN IMPENDING CONFLICT. ITS VALUE CANNOT BE OVERSTATED. THE TA GAVE US TIME TO EVALUATE AND RESOLVE A DEVELOPING TFC PROB. A CORRECT AND TIMELY RA WAS ISSUED WHICH WOULD HAVE PREVENTED A CLOSE CALL OR WORSE; HAD WE BEEN UNABLE TO ESTABLISH VISUAL CONTACT. SUPPLEMENTAL INFO FROM ACN 454834: I BELIEVE THE AIRLINER WAS SLOW IN ITS DSCNT; AND APCH CTL DIDN'T CATCH THE POSSIBLE CONFLICT.