2 SMAS HAVE AN NMAC WHILE ENRTE.

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I WAS FLYING A 035 DEG MAGNETIC COURSE AND CRUISING AT 5500 FT. I FIRST SIGHTED THE OTHER ACFT AT MY 10 O'CLOCK POS; AND APPROX MY ALT. IT WAS QUITE A WAYS AWAY. I STUDIED ITS PROFILE AND DECIDED IT MUST BE FLYING PARALLEL OR AWAY FROM ME. I CONTINUED MY SCAN; AND UPON COMING BACK TO IT; I NOTICED IT HAD MOVED TO 11 O'CLOCK AND BECOME LARGER. I CONCENTRATED ON IT TO TRY AND DETERMINE ITS COURSE AND ALT. AS I SAW THAT WE WERE CLOSING ON EACH OTHER; I DECIDED TO INITIATE EVASIVE ACTION. I ENTERED A DSNDING L TURN; TO PASS BEHIND AND BELOW HIM. HE BUZZED PAST ME; AT MY ALT; VERY; VERY CLOSE. IT SEEMED THAT HIS 12 INCH N NUMBERS WERE ABOUT 1 INCH HIGH IN MY WINDSHIELD. I BELIEVE HE MAY HAVE ENTERED A L TURN TO AVOID A COLLISION; BUT I AM NOT SURE OF THIS. I ESTIMATE HIS COURSE TO HAVE BEEN 150 TO 170 DEGS. I DO NOT KNOW WHEN; IF EVER; HE SAW ME; OR IF HE RECOGNIZED THE COLLISION POTENTIAL. I BELIEVE THAT MY INITIAL INCORRECT CONCLUSION THAT HE WAS FLYING AWAY FROM ME WAS BASED ON THE FACT THAT HE WAS AT THE SAME ALT AS ME; AND MY NAIVE ASSUMPTION (ALTHOUGH I'VE GOT ENOUGH HRS TO KNOW BETTER) WAS THAT IF WE WERE BOTH FOLLOWING THE HEMISPHERICAL RULE; AND AT THE SAME ALT; WE MUST BE HEADED BASICALLY THE SAME DIRECTION. I HADN'T REALLY CONSIDERED THAT HE COULD BE UP TO 144 DEGS OFF MY COURSE AND STILL BE FOLLOWING THE RULE. WHEN I DID RECOGNIZE HIS ACTUAL HDG; I WAS EITHER TOO SLOW TO REACT; OR MISJUDGED HIS RANGE. MY INTENTION WAS TO AVOID HIM WITH PLENTY OF ROOM; BUT INSTEAD WE CAME FAR TOO CLOSE TO EACH OTHER. WHEN I REFLECT ON HOW I COULD HAVE MADE THE SIT SAFER; WHAT I FIND MOST FRUSTRATING IS THAT I SAW HIM; BUT ALMOST FAILED TO AVOID. I HAVE PARTICIPATED IN THE FLT PHYSIOLOGY COURSE HELD BY THE AIR FORCE FOR GA PLTS; AND THEY DISCUSSED EXACTLY THIS THING. IT WAS ILLUSTRATED USING SEQUENTIAL SLIDES. IT SIMPLY WAS VERY DIFFICULT FOR ME TO RECOGNIZE IN THE REAL SIT. IT IS NOT CLR TO ME HOW TO DO IT BETTER NEXT TIME.