MD83 FLT CREW DURING VFR APCH TO MMSD RWY 16 HAS DIFFICULTY UNDERSTANDING THE CTLR DUE TO LANGUAGE DIFFERENCES; EXECUTES A 360 DEG TURN WITHOUT PERMISSION; LANDS SAFELY.

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CONTACTED MMSD APCH CTL. CTLR WAS VERY HARD TO UNDERSTAND BY MYSELF AND COPLT. WE HAD TO CLARIFY MANY CLRNCS AS DID THE 2 ACFT AHEAD OF US. THE CTLR; IN A NON RADAR MODE; SEEMED TO BE QUITE BUSY HANDLING US AND THE 2 ACFT AHEAD OF US. TO ADD TO THE CTLR'S PROBS HE HAD TO BUILD IN ENOUGH SPACING TO ALLOW THE LNDG ACFT TO BACK TAXI DUE TO NO TXWYS AT THE ROLLOUT END OF THE RWY. TO GET THE SPACING BTWN US AND THE LNDG ACFT; THE CTLR ASKED US IF WE HAD THE RWY; WHICH WE DID; AND THEN GAVE US THE CLRNC TO DSND VFR AND ENTER A L TFC PATTERN FOR RWY 16. AT THIS TIME WE WERE AT 5000 FT; 10 MI OUT LOOKING DOWN AT RWY 16. WE DIDN'T REALLY KNOW EXACTLY WHAT HE WANTED US TO DO WITH THIS 'L HAND TFC PATTERN.' WE TOLD HIM WE WERE GOING TO DO A L 360 DEG TURN TO THE RWY. SO WE STARTED A DSNDING L-HAND TURN AND ROLLED OUT ON GLIDE PATH LINED UP WITH RWY 16. AT THIS POINT THE CTLR CAME UNGLUED; 'WHO TOLD YOU TO DO A L 360?' AND SOME OTHER THINGS IN SPANISH THAT NEITHER OF US UNDERSTOOD. I THINK HE WAS CONCERNED THAT THE LNDG ACFT HAD TO BACK TAXI AND WE WOULD HAVE TO GO AROUND. HE THEN TOLD US TO CONTACT TWR. WE THEN LANDED UNEVENTFULLY.