FO OF A LEARJET; LR60 MADE MISSED APCH IN RESPONSE TO A TCASII TA AND SUBSEQUENT OBSERVATION OF A CESSNA PARALLEL TO HIS ILS APCH COURSE INSIDE OF THE FINAL APCH FIX.

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THE FLT WAS UNEVENTFUL UNTIL ON APCH INTO MVY. APCHING MVY THE WX WAS OBTAINED VIA ATIS AND WAS RPTED AS CLR SKIES 10 MI VISIBILITY WINDS 310 DEGS AT 4 KTS ALTIMETER 29.99. UPON REACHING THE ARPT THE WX HAD CHANGED SIGNIFICANTLY TO A 700 FT OVCST LAYER. I DON'T BELIEVE THIS IS UNUSUAL FOR MVY. THE DECISION TO DO THE ILS TO RWY 24 WAS AGREED UPON BY BOTH THE CAPT AND MYSELF. THIS APCH SET UP AND BRIEFED WELL BEFORE REACHING THE ARPT. BEFORE REACHING THE CLASS C AIRSPACE OF MVY IT WAS QUITE OBVIOUS THAT MVY WAS VERY BUSY JUST BY THE AMOUNT OF RADIO TFC ON APCH CTL (IT WAS JUL/SAT/00). WE WERE VECTORED TO AND WERE CLRED FOR THE ILS RWY 24; WHICH WE DID. JUST PRIOR TO AND BEFORE REACHING THE FINAL APCH FIX (FAF) WE WERE HANDED OFF TO AND TOLD TO CONTACT MVY TWR. BECAUSE OF RADIO TFC SATURATION WE WERE NOT ABLE TO IMMEDIATELY CONTACT TWR CTL AS INSTRUCTED. JUST AFTER REACHING THE FAF/GS INTERCEPT AND WHILE DSNDING ON THE GS WE RECEIVED A TA ALERT ON THE TCASII. IN THE INTEREST OF SAFETY I ARRESTED MY DSCNT ON THE GS. THE CAPT ACQUIRED A HIGH WING CESSNA IN FRONT OF AND BELOW US IN THE ILS APCH CORRIDOR. TO CONTINUE THE DSCNT ON THE GS WOULD HAVE AT THE VERY LEAST RESULTED IN A NEAR MISS AND AT THE VERY WORST A MIDAIR COLLISION. AS PF I ELECTED TO GO MISSED APCH. IN THE 10-15 SECONDS THAT HAD ELAPSED FROM OUR HDOF FROM APCH TO TWR WE WERE VERY BUSY BOTH FLYING AND VISUALLY ACQUIRING OUR TA. AT THE VERY FIRST OPPORTUNITY TO CONTACT TWR BECAUSE OF RADIO TFC SATURATION WE DID. BECAUSE I HAD ELECTED TO GO MISSED APCH THE CAPT CHKED IN WITH MVY TWR; 'LTT WITH YOU ILS RWY 24 GOING MISSED APCH.' WE PROCEEDED TO THE MISSED APCH AND DID THE PUBLISHED MISSED APCH. AT NO TIME PRIOR TO THIS DID WE CANCEL IFR NOR ACCEPT A VISUAL APCH. UPON OUR CHK IN WITH TWR THAT WE WERE GOING MISSED APCH WE WERE QUERIED AS TO WHY? THEY WERE INFORMED THAT WE HAD VISUALLY ACQUIRED TFC IN THE APCH CORRIDOR AND IN THE INTEREST OF SAFETY HAD ELECTED TO GO MISSED APCH. WE REQUESTED FURTHER INSTRUCTIONS AND RECEIVED VECTORS BACK TO THE ILS RWY 24 WHICH WE DID AND LANDED AT MVY. IN CONCLUSION I CAN ONLY ASSUME THAT THE CESSNA THAT WAS IN OUR APCH CORRIDOR WAS ON A SPECIAL VFR CLRNC BECAUSE OF THE 700 FT CEILING. MY DECISION TO GO MISSED APCH WAS APPROPRIATE AND IN THE INTEREST OF SAFETY CALLED FOR.