B727-200 FLC RPTS ON THEIR DRIFTING OFF A-766 AFTER RECEIVING RADAR VECTORS TO A FIX FROM MERIDA CTR. THEY WERE NOT RNAV EQUIPPED FOR DIRECT TO A FIX OR INTXN. FLT WAS FROM CANCUN TO DFW VIA IAH.

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WAS CLRED FROM CUN TO DFW VIA; AS FILED (FLT PLAN RTE WAS UJ52 EDGAR A766 SBI DIRECT IAH CQY2DFW FL350). RWY 12; REACHING 2000 FT; L TURN. TOOK OFF AND IN L TURN CUN SAID DIRECT TO KEHLI INTXN; I SAID NOT RNAV EQUIPPED; HE SAID DIRECT KEHLI INTXN; I SAID WE NEED A HEADING. HE SAID RADAR VECTOR TO KEHLI. I SAID FOR HIM TO TELL US WHEN WE WERE ON COURSE; HE SAID OKAY. AROUND 100 MI NW OF COZUMEL AND CANCUN VORS; THEY WERE STARTING TO BE VERY ERRATIC IN SIGNALS (DME AND VOR). ABOUT PM53Z MERIDA CTR LOST RADAR CONTACT AND SAID WE WILL BE OVER KEHLI IN 4 MINS; THEN TURN 5 DEGS R FOR ON COURSE AND CONTACT NEW YORK COMMERCIAL RADIO 130.7 AT KEHLI. WE DID THAT BUT WE HAD NO NAVAIDS AND WENT BY INFO; DEAD RECKONING AND PILOTAGE. NEW YORK SAID CONTACT ZHU 25 DEGS N. WE GUESSED THAT POINT. WE CALLED ZHU AT 25 DEGS N AND HAD NO CONTACT. WE KEPT CALLING AND FINALLY ACR Y AIRLINES ANSWERED AND RELAYED TO HOUSTON OUR POS. WE SET IN THE 218 DEG RADIAL OFF OF LEV VOR; KELPP INTXN AND WE ENDED UP XING THE 218 DEG RADIAL; BUT THE DME WAS READING NOTHING AND THEN THE NUMBERS WERE CONSTANTLY ROLLING. FINALLY HOUSTON SAID RADAR CONTACT YOU ARE 45 MI W OF COURSE AND TURN R IMMEDIATELY TO SOME HEADING (?). WE FLEW THAT HEADING FOR MAYBE 2 MINS AND THEN THEY CLRED US DIRECT TO SBI VOR. I SAID WE'RE NOT RNAV EQUIPPED; AND THEN THEY GAVE US A HEADING; AND WAS TO CALL ZHU ON THE GND AT DFW AND SPEAK TO MR X. I TALKED TO HIM AND HE THOUGHT WE WERE RNAV EQUIPPED I GUESS; AND ASKED WHY WE WERE OFF COURSE 45 MI; THAT THERE WAS AN ACR Y ACFT WHOSE AIRSPACE WE VIOLATED. I EXPLAINED WHAT HAPPENED AND THAT IT WAS NOT OUR FAULT; NO RNAV; RADAR VECTORS TO A FIX; NO VORS TO GET A GOOD WIND CORRECTIONAL ANGLE (THE NIGHT BEFORE WE HAD 25-30 DEG WIND CORRECTION ANGLE) AND I ASKED WHY THEY SHOWED THAT WE WERE LNDG AT IAH ARPT; AND WHY THE CTLRS WERE GIVING US DIRECT TO POINTS THAT WE COULDN'T RECEIVE; WE WERE NOT RNAV EQUIPPED; AND HE COULDN'T EXPLAIN WHY. HE FINALLY UNDERSTOOD; BUT SAID HE HAD TO FILE AN OCEANIC FIR OFF COURSE RPT. THE NEXT DAY I CALLED MR X. HE COULDN'T GIVE A LATITUDE/LONGITUDE POS; BUT HE WAS VERY NICE; AND SAID THAT WE WERE NOT IN ACR Y'S AIRSPACE. HE WAS 90 MI AHEAD OF US. THAT WAS NOT THE PROB; BUT THAT WE WERE OUT OF OUR AIRSPACE; SO HE STILL HAD TO FILE A RPT. HE ALSO TALKED TO NEW YORK COMMERCIAL RADIO AND THEY CONFIRMED OUR RPT OVER KEHLI. HE TALKED TO MERIDA CTR AND CANCUN. THERE WERE A FEW CONFLICTING STORIES HE TOLD ME; BUT HE COULDN'T TELL ME EXACTLY; BUT HE UNDERSTOOD THE WHOLE SIT. RECOMMENDATION: VORS AND DME'S WITH BETTER COVERAGE; RNAV EQUIP IN ACFT AND NO RADAR VECTORS TO POINTS WITH NO RADAR COVERAGE.