NMAC. A NO FLT PLAN ACFT BEING VECTORED THROUGH CLASS B AIRSPACE HAS AN NMAC WITH AN ACR.

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I WAS FLYING GRUMMAN AA5A FROM GEORGETOWN; TX (TO4) TO PONCA CITY; OK (PNC). I TOOK OFF AND PROCEEDED NBOUND; CONTACTING GRAY APCH AND REQUESTED FLT FOLLOWING TO PNC. I WAS GIVEN A SQUAWK AND PROCEEDED ON COURSE TO ACT; THENCE TO THE DFW AREA. I WAS HANDED OFF TO REGIONAL APCH; CLRED INTO THE CLASS B AIRSPACE AND DIVERTED TO THE W TO AVOID THE DFW ARPT AREA; BEING TOLD THAT I WOULD LATER RECEIVE A VECTOR TAKING ME TOWARD DENTON; TX. I DIVERTED AS INSTRUCTED AND FLEW THE GIVEN HDG AND ALT OF 3500 FT USING THE CURRENT ALTIMETER SETTING FURNISHED BY REGIONAL APCH. I AM NOT SURE OF THE TIME; BUT IT WAS APPROX XA40Z THAT I SAW A COMMERCIAL AIRLINER VERY CLOSE AT MY 1 O'CLOCK POS AND SLIGHTLY HIGH. I STARTED A DSCNT TO AVOID THE AIRLINER AND IT STARTED WHAT APPEARED TO BE A RAPID DSNDING L TURN WHICH PUT HIM ON A COLLISION COURSE WITH ME. I IMMEDIATELY WENT INTO ABOUT A 90 DEG R BANK DSNDING BECAUSE I THOUGHT THAT I WOULD CERTAINLY ENCOUNTER SOME JETWASH AFTER HE PASSED ME. HOWEVER; I DID NOT. AS MY NOSE WAS SWINGING TO THE R AND SWEEPING ALONG THE ENTIRE BODY OF THE JET; I SAW THAT IT WAS A B-737 ACFT. I WOULD ESTIMATE THAT WE MISSED EACH OTHER BY NO MORE THAN 150 FT. THAT ESTIMATE COMES FROM 23 YRS IN THE UNITED STATES AIR FORCE WITH SEVERAL YRS OF CLOSE; FIGHTER TYPE FORMATION FLYING; AND YRS OF AIR REFUELINGS; SO I THINK THAT MY ESTIMATE OF DISTANCE IS FAIRLY ACCURATE. BEING THAT CLOSE TO ANOTHER ACFT IS NOTHING NEW TO ME. HOWEVER; I DISLIKE 2 ACFT TRYING TO OCCUPY THE SAME AIRSPACE AT THE SAME TIME; ESPECIALLY IF ONE OF THEM IS MINE! AFTER I REGAINED HDG AND ALT I TOLD REGIONAL APCH THAT I HAD JUST HAD A NEAR COLLISION AND HAD HAD TO PERFORM VIOLENT EVASIVE ACTION TO AVOID CONTACT WITH THE AIRLINE JET. ALL I GOT WAS A 'ROGER.' I PROCEEDED ON THE ASSIGNED HDG AND WHEN I WAS GIVEN A HDOF FREQ I INQUIRED IF THERE WASN'T SOME INDICATION ON APCH'S EQUIP WHICH INDICATED AN UNSAFE CONDITION AND POSSIBLE COLLISION. AT THIS TIME ANOTHER CTLR ANSWERED AND SAID THE SIT WAS BEING INVESTIGATED. I AM ALSO WONDERING WHY THE AIRLINER'S TCASII DIDN'T ALERT HIM; BUT IT WAS PROBABLY BECAUSE I WAS NEVER DIRECTLY IN FRONT OF HIM. I WAS OFF TO HIS L; AND WHEN HE WENT INTO HIS DSNDING L TURN I NEVER WOULD HAVE BEEN DIRECTLY IN FRONT OF HIM UNTIL IMPACT; AND I AM SURE THAT THERE WOULD HAVE BEEN AN IMPACT IF I HADN'T TAKEN THE EVASIVE ACTION WHICH I DID. I THINK THAT THE ORIGINAL CTLR MAY HAVE BEEN IN TRAINING; AND/OR UNDER SOME STRAIN. HIS SPEECH WAS STRESSFUL AND INSTRUCTIONS WERE GIVEN IN A STACCATO MANNER WHEN THERE WAS NO NEED FOR THAT TYPE OF DELIVERY BECAUSE IT DIDN'T SEEM TO BE THAT BUSY. I THINK THAT HE WAS PERHAPS RELIEVED BY HIS SUPVR AFTER THE INCIDENT.