MD88 ACFT IN DSCNT IN CLASS C AIRSPACE HAD TCASII RA AND TOOK EVASIVE ACTION. ATC HAD MADE NO EFFORT TO PROVIDE FOR SEPARATION AND RPTR CAPT THINKS THERE WAS A BREAKDOWN IN INTERCOORD BTWN THE TWR AND TRACON.

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WHILE BEING RADAR VECTORED TO LOC RWY 3 AT GSP; DSNDING FROM 5000 FT MSL TO OUR ASSIGNED ALT OF 4000 FT MSL WE RECEIVED A TCASII TA FOR TFC AT 6 MI AT 11-11:30 O'CLOCK POS. THE TFC INDICATED 3500 FT MSL AND CLBING. WE ESTABLISHED VISUAL CONTACT WITH A JETSTAR SIMULTANEOUSLY WITH A TCASII RA 'CLB.' THE JETSTAR VISUALLY APPEARED TO BE ON A COLLISION COURSE WITH US (NO VISIBLE MOVEMENT ON THE WINDSCREEN) SO THE RA CLB WAS FOLLOWED ALONG WITH A SLIGHT R TURN TO AVOID A COLLISION. OUR BEST ESTIMATE OF VERT SEPARATION AT THE MERGE WAS APPROX 500 FT WITH US HAVING CLBED TO AVOID THE TFC. WE RPTED THE NEAR MISS WITH GSP APCH AND LANDED UNEVENTFULLY. I CAN'T PINPOINT OUR LOCATION RELATIVE TO GSP ARPT BUT THE INCIDENT OCCURRED BTWN 3500-4500 FT MSL AS WE WERE ENTERING THE GSP ARPT CLASS C AIRSPACE. THE JETSTAR ACFT DEPARTED VFR FROM GREENVILLE DOWNTOWN ARPT CLASS D AIRSPACE WHICH IS WITHIN THE GSP CLASS C AIRSPACE. I 'THINK' WE RECEIVED A TA FROM GSP APCH BUT IF WE DID IT WAS AFTER THE RA AND DURING OUR EVASIVE MANEUVERING. THERE WAS NO EFFORT MADE BY GSP APCH TO PROVIDE FOR SEPARATION FROM THE JETSTAR. DETERMINING THE EXACT CAUSE OF THIS SIT IS DIFFICULT FOR ME SINCE THERE ARE 2 ARPTS IN VERY CLOSE PROX; AND DIFFERENT AIRSPACES WHICH OVERLAP. HOWEVER I BELIEVE THERE WAS A BREAKDOWN IN COM BTWN GREENVILLE DOWNTOWN TWR AND GSP TRACON. ALSO SOME COMPLACENCY MAY HAVE BEEN INVOLVED DUE TO THE DAY BEING A SUNDAY WITH PERFECT WX. THE ONE SINGLE MOST DECISIVE THOUGHT RESULTING FROM THIS IS THE ABSOLUTE EFFECTIVENESS OF THE TCASII AND IT SHOULD BE A NO-GO ITEM FOR EVERY PART 121 CARRIER IF IT IS INOP. FROM MY EXPERIENCE IN MIL AIR TO AIR COMBAT AND INTERCEPTS; I TRULY BELIEVE THERE WOULD HAVE BEEN A COLLISION WITHOUT EVASIVE MANEUVERING. NOTE: GSP TRACON AREA SUPVR WAS NOT GOING TO FILE A NEAR-MISS RPT UNTIL I INSISTED OVER THE PHONE THAT HE DO SO. ALSO WE RPTED THE NEAR MISS TO THE CTLR IMMEDIATELY AFTER THE INCIDENT ON VHF FREQ.