SMA PLT ALLEGES THAT HE HAD AN NMAC WITH SMT WHILE ON APCH TO FUL ARPT; BOTH ACFT ON IFR FLT PLANS.

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I WAS MAKING THE VOR APCH TO FULLERTON AND WAS BEING VECTORED TO FINAL BY COAST APCH. I WAS AT 3000 ASSIGNED ND HAD JUST BEEN GIVEN APCH CLRNC AND A TURN TO FINAL. I BEGAN THE TURN AS NORMAL AT WHICH TIME THE CTLR REQUESTED A GOOD RATE OF TURN. I IMMEDIATELY DISENGAGED THE AUTOPLT AND ROLLED INTO A 45 DEG TURN. DURING THIS APCH PERIOD I HEARD ANOTHER ACFT ALSO ON FREQ. THE SMA Y WAS ALSO AT 3000 AND BEING VECTORED FOR THE APCH. I BELIEVED HIM TO BE TO THE NW OF MY POS ALTHOUGH HE WAS NEVER GIVEN AS TFC. I WAS BTWN LAYERS; BUT DID NOT SEE ANY TFC. I COMPLETED THE APCH AND LNDG WITHOUT INCIDENT. WHILE ON THE RAMP I WAS APCHED BY THE PLT OF THE SMA Y; HE APPEARED VERY SHAKEN. HE INDICATED THAT WE HAD MISSED COLLIDING BY ABOUT 200-500 FT WHILE I WAS TURNING TO FINAL. HE THOUGHT THAT I HAD SEEN HIM AND TURNED SHARPLY TO AVOID HIM. I WAS NOT AWARE HE WAS THERE. HE DID NOT SEE ME UNTIL HE SAW THE BELLY OF THE SMT X IN THE TURN. WE WERE BOTH IFR AND NEITHER OF US HAD BEEN GIVEN THE OTHER AS TFC.