NMAC BTWN 2 SMA TRAINING ACFT AT NON TWR ARPT.

Narrative

MY STUDENT AND I WERE GOING VFR FROM UBG UNDER FLT FOLLOWING AND ASKED FOR A VFR ILS APCH TO MMV. APCH CTL ADVISED US THAT WE SHOULD PROCEED DIRECT TO THE LOM; BUT NO TFC SEPARATION WOULD BE PROVIDED. WE WERE CLRED FOR THE APCH BUT MAINTAIN VFR AT LOM; SO WE STARTED PROC TURN OUTBOUND AND ADVISED APCH. AT APPROX SAME TIME; AN SMA CALLED APCH FOR VECTOR. HE WAS ADVISED HE WAS #2 FOR APCH. WE WERE THEN INSTRUCTED TO CONTACT LCL CTAF AND RPT BACK TO APCH ON THE MISSED APCH CLB. WE THEN SWITCHED TO CTAF AND TURNED INBOUND. WE ADVISED MMV WE WERE INBOUND. AT LOM WE ADVISED AGAIN LOM INBOUND. ABOUT 1 MIN PASSED AND I HEARD THE SMA ADVISE LOM INBOUND. I REPLIED TO THEIR CALL THAT WE WERE 2 MI OUT INDICATING 90 KTS. THE SMA ADVISED US THAT HE HAD US IN SIGHT! WE WERE STILL INBOUND AT APPROX 500 FT MSL WHEN I SAW THE SMA PASSING US ON THE L. AS HE PASSED; I TOOK THE CTL FROM THE STUDENT AND PROCEEDED TO MAKE A CLBING R TURN TO RESOLVE ANY OTHER PROB FROM THE SMA. I FEEL THE SMA FAILED TO OBSERVE ANY SEPARATION FROM US; WE WERE #1 ON THE APCH. IF HE WOULD HAVE SAID HIS INTENTION OR ADVISED US OF A PROB WE WOULD HAVE BROKEN OFF APCH. I HAD ADVISED HIM OF OUR SPD SO HE SHOULD HAVE SAID HE PLANNED ON OVERTAKING US. AS WE CLBED OUT I SAW THE SMA EXECUTE A MISSED APCH AT APPROX 400 MSL; SO I KNOW THEY HAD NO ENG PROBS. POSSIBLE CORRECTION TO PROB IS HIGHER PROC TURN ALT SO APCH COULD SEE ACFT AS IT IS ON PROC; SO OTHER ACFT WOULD NOT BE TURNED IN WITH VECTOR TO FOLLOW OTHER ACFT. I DON'T KNOW OF ANYTHING I COULD HAVE DONE OTHER THAN BEEN IFR; BUT THAT STILL WOULDN'T STOP ANOTHER VFR ACFT FROM FLYING APCH.