A BONANZA A36 PLT ON A VISUAL APCH TOOK EVASIVE ACTION TO AVOID COLLISION WHEN A B737 ALSO ON A VISUAL APCH DSNDED OVER HIM.

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I WAS FLYING MY BONANZA A36. I WAS CLRED BY EL PASO APCH TO 5000 FT AGL AND ON NOTIFYING HIM I HAD FIELD IN SIGHT AT ABOUT XA45; HE CLRED ME FOR VISUAL APCH ON RWY 26L AND ASKED ME TO CONTACT TWR. I CONTACTED TWR AND HE CLRED ME TO LAND ON RWY 26L. I WAS LINED UP ON THE RWY AND ABOUT 3 MI OUT DSNDING WHEN MY TCASII IDENTED ANOTHER ACFT AT 600 FT ABOVE ME AND 1 1/2 MI TO MY L AT 9 O'CLOCK POS. THE TWR THEN CLRED THE B737 FOR VISUAL APCH ON RWY 26L AND INFORMED ME IN THE SAME XMISSION THAT THE B737 TFC WOULD PASS IN FRONT OF ME. THE B737 PLT REPLIED AND STATED HE DID NOT HAVE TFC IN SIGHT (ME). AT THIS TIME; HE WAS 400 FT ABOVE AND ABOUT 1/4 MI FROM ME (ON TCASII AND VISUAL) AND DSNDING DIRECTLY FOR ME. I TURNED R TO AVOID HIM AND DSNDED. AS HE PASSED DIRECTLY OVER ME AND 300 FT ABOVE ON TCASII; I TOLD HIM I WAS IMMEDIATELY UNDER HIM AND CONTINUED EVASIVE ACTION. HE THEN PASSED AHEAD OF ME; AT WHICH TIME WE WERE ABOUT 1 1/2 MI FROM TOUCHDOWN. I THEN DID A 360 DEG TURN TO THE L TO INCREASE SEPARATION FLYING THROUGH HIS WAKE TURB AND THEN PROCEEDED TO LAND AFTER THE B737 WAS CLR OF THE RWY. THE B737 PLT REPLIED AFTER LNDG THAT THEY NEVER SAW TFC. I FEEL CLRING BOTH ACFT TO VISUAL APCH WITHIN 400 FT VERT SEPARATION WAS AN ERROR AND HAD I NOT TAKEN EVASIVE ACTION; HE WOULD HAVE DSNDED RIGHT ON TOP OF ME WITH DIRE CONSEQUENCES TO BOTH ACFT. CTLR SHOULD HAVE ANTICIPATED THE PROB AND NOT CLRED US BOTH WITHIN SUCH CLOSE PROX.