A SMALL ACFT PILOT ON APPROACH TO AXH EXPERIENCED NMAC WITH ANOTHER SMALL ACFT.

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I WAS ON FINAL APCH TO RWY 9 AT AXH ARPT ON AN INST APCH IN INST CONDITIONS WITH HOUSTON APCH. WHEN I DSNDED INTO VFR CONDITIONS; I CANCELED IFR AND TERMINATED WITH HOUSTON. I THEN ANNOUNCED ON CTAF FOR AXH THAT I WAS ON FINAL FOR RWY 9. IMMEDIATELY AN AIRPLANE ANNOUNCED HE HAD JUST TAKEN OFF RWY 27 AND WAS CLBING OUT FOR A L TURN PATTERN. I SAW HIM AND HE WAS NO FACTOR. HOWEVER; THIS SAME PLANE SAID HE BELIEVED THERE WAS ANOTHER PLANE THAT WAS GOING TO TAKE OFF RWY 27. I WAS ON VERY SHORT FINAL WITH STROBE LIGHTS; LNDG LIGHTS; AND IN LNDG CONFIGN. JUST AS I WAS ATTEMPTING TO LAND THE SECOND PLANE WAS TAKING OFF RWY 27 WHO DID NOT HOLD TO LNDG TFC. HE GOT ON THE RADIO AFTER LIFT-OFF AND SAID HE WOULD DIVERT TO 'MY R;' OR L TURN TFC. AN EMER OCCURRED AS WE WERE TOO CLOSE TO CONTINUE MY LNDG ON THE RWY AND THUS I DID L RUDDER; STRAIGHTEN OUT; AND LANDED ON THE PARALLEL TXWY. THERE WAS NO OTHER TFC ON THE GND AND NO FURTHER INCIDENT OCCURRED. WINDS WERE LIGHT/VARIABLE WITH VFR CONDITIONS AND GOOD VISIBILITY.