CPR LTT HAS CLOSE CONFLICT WITH A BIPLANE DOING AEROBATICS NEAR AND OR UNDER THE IAH TCA.

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WHILE ENRTE FROM IAH TO GLS A MIDAIR NEAR MISS OCCURRED. WHILE AT 3000 FT ON A 140 DEG HDG FOR DIRECT GLS ABOUT 20 NM AND 200 KTS NW OF GLS UNDER VFR CONDITIONS (NO CEILING AND UNRESTR VISIBILITY) WE WERE TALKING TO HOUSTON APCH CTL. ATC ISSUED A TA. IT WAS FOR A LEAR; ALT UNKNOWN AT 12 O'CLOCK AND A MI. ATC SAID WE COULD CLB AS NECESSARY. BOTH OF US LOOKED FORWARD AND WE BOTH SAW WHAT APPEARED TO BE A BLACK ACFT AT 12 O'CLOCK LOW (ESTIMATE 500-800 FT AGL) MOVING FROM L TO R; PERPENDICULAR TO OUR FLT PATH. NEITHER ONE OF US EVER SAW A LEAR. I AM NOT SURE IF ATC HAD CONFUSED THE LEAR WITH THE BLACK PLANE OR NOT. WITHIN APPROX A MIN OF SEEING THAT ACFT PASS FROM L TO R; A BLACK BIPLANE WAS SIGHTED AT OUR 12 O'CLOCK. IT HAD JUST PERFORMED A RAPID VERT MANEUVER UP TO ABOUT 3000 FT MSL. OUR FLT PATH POINTED US TOWARD EITHER THE UNDERSIDE OR THE TOP OF THE ACFT; CLRLY DEFINING THAT IT WAS A BIPLANE. INITIALLY; IT WAS UNKNOWN WHAT ITS ORIENTATION WAS SINCE IT WAS AT THE TOP OF THE MANEUVER AND APPROX AT OUR ALT; APPROX 1500 FT IN FRONT OF US. THE BEST COURSE OF ACTION BASED ON THE EXISTING CONDITIONS AND FACTORS WAS A DSNDING R TURN FOR EVASIVE ACTION. THAT WAY I WAS STILL ABLE TO MAINTAIN SOME VISUAL CONTACT WITH THE BIPLANE WHILE AVOIDING IT. WE PASSED UNDER THE BIPLANE BY ABOUT 500 FT WITH IT ON OUR L WING ABOUT 200-300 FT HORIZLY. AFTER WHICH WE RETURNED TO 3000 FT DIRECT TO GLS. I TRIED TO CALL ATC TWICE AND WAS STEPPED ON. FINALLY; ON A THIRD CALL I WAS ABLE TO GET THROUGH AND TOLD ATC THAT WE HAD TO MAKE AN EVASIVE MANEUVER TO AVOID A BIPLANE BY ABOUT 500 FT; AND THAT WE DSNDED ABOUT 500 FT. WE CONTINUED ON TO GLS AND BY NOW WE WERE AT ABOUT 10 NM FROM GLS. THE REST OF THE FLT WAS COMPLETED NORMALLY AND UNEVENTFULLY.