BE1900 HAS NMAC WITH TWIN OTTER IN THE TCA AT ST MARTIN; FO.

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WE WERE CLRED FOR TKOF FROM RWY 9 BY JULIANA ATC WITH INSTRUCTIONS TO TURN R TO A HDG OF 200 DEGS AND TO MAINTAIN THAT HDG UNTIL REACHING 5000 FT; THEN CONTINUE THE R TURN ON COURSE TO SJU AND CLB TO 10000 FT. WE WERE ESTABLISHED ON A HDG OF 200 DEGS AND CLBING THROUGH 1500 FT MSL WHEN WE FORTUNATELY SIGHTED A TWIN OTTER DIRECTLY IN FRONT OF US; AT OUR ALT. WE MADE AN EVASIVE TURN TO 160 DEGS AND PASSED BEHIND THE TWIN OTTER (WHICH WAS ON A R DOWNWIND ARR TO RWY 9 AT ST MARTIN). I BELIEVE THE CONTRIBUTING FACTORS TO THIS INCIDENT ARE A VERY OVERLOADED AIR TFC CTLR; THE MOUNTAINS OBSTRUCTING OUR VISION OF THE TFC; THE APPARENT LACK OF OPERABLE XPONDER ON THE TWIN OTTER (OUR TCASII DID NOT DISPLAY THE TFC; ALTHOUGH IT DID DISPLAY OTHER TFC IN THE AREA); AND THE LACK OF RADAR IN THIS VERY BUSY AIRSPACE. JULIANA (ST MARTIN) ATC UTILIZES ONLY 1 FREQ FOR ATIS (WX); CLRNC DELIVERY; ENG START; GND CTL; TWR; APCH AND DEP CTL. IT IS NEEDLESS TO SAY THERE ARE MANY BLOCKED COMS; AND THE SINGLE CTLR IS OFTEN OVERWHELMED. IN THE EARLY AFTERNOON THERE ARE TYPICALLY 6-8 JETS AND 10-15 TURBOPROPS; AND MULTIPLE CPR JETS.