SMA Y NON ADHERENCE TO ATC INSTRUCTIONS HAD NMAC WITH SMA X IN TFC PATTERN. SEE AND AVOID CONCEPT.

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SMA X APCHING FROM THE NE; I CALLED DRAKE TWR TO RPT 10 MI AND LNDG WITH INFO JULIETTE. TWR AGAIN ASKED FOR POS. REPLY 9 MI NE LNDG WITH INFO. TWR INSTRUCTED TO ENTER R DOWNWIND FOR LNDG 34. ON APCHING MIDFIELD R DOWNWIND; I HEARD SMT Y RPTING VOR FOR LNDG. TWR INSTRUCTED THE SMT Y TO ENTER L DOWNWIND FOR 34 AND #2 TO LAND BEHIND SMA X. I ANNOUNCED ENTERING R DOWNWIND AT MIDFIELD AND WAS CLRED TO LAND. THE SMT Y WAS INSTRUCTED TO EXTEND DOWNWIND AND AGAIN TOLD #2 FOR LNDG. ON MY ENTERING R BASE 34 WITH GEAR DOWN FOR LNDG; I WAS INSTRUCTED TO CANCEL LNDG CLRNC AND TO EXTEND MY DOWNWIND FOR #2 LNDG. I REPLIED (AS I WAS ON R BASE AND UNABLE TO CONTINUE DOWNWIND); I WILL HAVE TO DO A 360 (TO COMPLY WITH NEW LNDG SEQUENCE). TWR REPLIED TO START AN IMMEDIATE S TURN THAT THE SMT Y WAS DIRECTLY BENEATH ME. I TURNED S AND REPLIED THAT I HAD THE AIRPLANE IN SIGHT AND REQUESTED THE TWR TELEPHONE NUMBER. THE SMT Y LANDED. I HAD TO MANEUVER A 360 TURN AND LAND. UPON LNDG I CALLED THE TWR; TALKED TO THE CTLR; REQUESTED THE TAPE BE PULLED; TOLD HER I WANTED A COPY OF THE TAPE AND THAT THERE WAS NO EXCUSE FOR THE WAY THE LNDG SEQUENCE WAS HANDLED. THE CTLR REPLIED THAT THE TAPE HAD BEEN PULLED AND THE SUPVR WOULD CALL ME TOMORROW (SAT). I HAVE NOT HEARD FROM A SUPVR OR ANY TWR PERSONNEL. I CANNOT SEE WHAT ADVANTAGE WAS SERVED BY THE TWR CHANGING THE LNDG SEQUENCE OF 2 AIRPLANES; ESPECIALLY AT SUCH A LATE TIME IN THE LNDG SEQUENCE.