NMAC AS ACFT Y ON VISUAL APCH TO A NON TWR ARPT UNICOM MAKES MISSED APCH ACCOUNT ACFT X ON IAP NDB APCH HAD 'CUT HIM OFF.'

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INBOUND TO FALFURRIAS; TX (T18). WX WAS IFR. GIVEN DSCNT CLRNC TO 4000 FT MSL AND ISSUED HOLDING INSTRUCTIONS AT BKS RADIO BEACON TO HOLD S AS PUBLISHED AND EXPECT DELAYS FOR OTHER ACFT AHEAD MAKING THE NDB RWY 35 APCH AT T18. JUST AFTER ENTERING THE HOLD THE AC690 IN FRONT OF US CANCELED IFR AND WE WERE GIVEN APCH CLRNC. SINCE THE HOLDING PATTERN IS IN THE APCH COURSE I DECIDED TO DO THE APCH OUT OF THE HOLDING PATTERN; WHICH IS A LEGAL COURSE REVERSAL. WE PROCEEDED OUTBOUND APPROX 1 1/2 MINS AND THEN TURNED INBOUND AND JOINED THE APCH COURSE AND LETDOWN TO MDA. INITIAL GND CONTACT WAS MADE AT APPROX 1000 FT AGL WITH LOWER CLOUDS (APPROX 700 FT) AHEAD. ARPT WAS SIGHTED AND WE SWITCHED TO UNICOM AT WHICH TIME WE HEARD THE AC690 CALLING MISSED APCH BECAUSE WE HAD CUT HIM OFF. THIS WAS ON ABOUT A 4-5 MI FINAL. HE HAD CANCELED IFR APPROX 3-4 MINS PREVIOUSLY. HOW WE GOT INTO THIS SIT I DO NOT KNOW. GIVEN THE APCH SPD OF THE AC690 AND THE 3-4 MINS FROM THE TIME HE CANCELED UNTIL WE MET I THINK HE MAY HAVE GONE PAST THE 10 MI ALLOWED FOR THE APCH.