A B757 FLT CREW EXPERIENCED A TCASII RA WHILE DSNDING.

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WAS FLYING THE SURFN 7 STAR INTO PBI. WAS BTWN ORM AND SURFN; EXECUTING AN FMS VNAV DSCNT (ON AUTOPLT) TO CROSS SWOMP AT 8000 FT; AS PUBLISHED. WAS RAPIDLY APCHING FL180 (AT 2500+ FPM DSCNT) WHEN ATC ADVISED THAT AN UNIDENTED TARGET JUST POPPED UP ON HIS RADAR AT 17400 FT MSL AND LOOKED LIKE IT WAS GOING TO BE A CONFLICT. HE SUGGESTED I LEVEL AT FL180 UNTIL THE TARGET COULD BE VERIFIED CLR. I IMMEDIATELY HIT ALT HOLD SINCE WE WERE RAPIDLY APCHING FL180. THIS WAS ACCOMPANIED BY A TCASII TA. THE TFC WAS NOT IN SIGHT. DUE TO THE HIGH RATE OF DSCNT; THE AUTOPLT DIPPED SLIGHTLY BELOW FL180 AS IT CAPTURED THE ALT. DURING THE DIP BELOW FL180; WE GOT A TCASII RA CLB ADVISORY; WHICH WE EXECUTED AS DIRECTED. ATC ASSISTED US IN MONITORING THE OTHER ACFT. ATC ADVISED THAT THE OTHER ACFT WAS NOT IN RADIO CONTACT AND TOOK NO EVASIVE ACTION (NO HDG OR ALT CHANGES); LEADING US BOTH TO BELIEVE THE OTHER ACFT WAS UNAWARE OF THE INCIDENT. ATC DID A GREAT JOB WITH THE ADVANCE WARNING AND LIKELY PREVENTED A MORE SERIOUS ACCIDENT/INCIDENT FROM OCCURRING. THERE WASN'T MUCH TIME TO REACT AND THERE WOULD HAVE BEEN EVEN LESS TIME WITHOUT THE ATC ADVISORY.