FLC OF AN WDB CLBED OFF ASSIGNED CRUISING ALT IN RESPONSE TO TCASII AND OTHER ACFT SIGHTING.

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APPROX 20 MI NW OF MIQ WHILE IN RADAR CONTACT WITH SVZM CTL WE WERE CLRED DIRECT TO LODIR AFTER MIQ VOR; THEN FLT PLAN RTE TO MAINTAIN FL290. ABEAM ANGEL INTXN WE WERE CLRED TO FL330. PRIOR TO THE POINT WHERE OUR DIRECT RTE FROM MIQ VOR TO LODIR INTERSECTED UA 315 FROM KUMUT TO ALBOG WE OBSERVED AN ACFT ON TCASII 40 MI TO OUR L AND SLOWLY CONVERGING WITH US. THIS TFC TURNED OUT TO BE ALSO A B767 WHICH DEPARTED MIA 6 MINS AHEAD OF US; AND WAS ALSO AT FL330. WE WERE ABLE TO MAINTAIN VISUAL CONTACT WITH HIM AT ALL TIMES. FO WAS IN 80 MI RANGE ON HIS HSI; FO WAS THE RELIEF PLT IN THE CAPT SEAT AS CAPT HAD STARTED HIS CREW REST. IT APPEARED THE ACFT WAS DRIFTING OUR WAY AND SVZM CTL WAS QUESTIONED ABOUT THE TFC; THEY STATED IT WAS ON A DIFFERENT RTE. FO WENT TO THE 10 MI SCALE AND STATED THAT IF THE TFC BREAKS THE 5 MI ARC HE WOULD START A CLB. SOON AFTER THAT THE TFC CAME INSIDE THE 5 MI ARC AND FO STARTED A CLB. AT APPROX 34200 FT THE TFC PASSED UNDER AND SLIGHTLY IN FRONT OF OUR ACFT. AT ABOUT THIS TIME CAPT RETURNED TO THE COCKPIT TO INQUIRE ABOUT THE ALT CHANGE. THERE WAS NO TA OR RA AT ANY TIME. WE WERE THEN ABLE TO ESTABLISH RADIO CONTACT WITH THE 767 ON 130.55. THEY CONFIRMED THEY WERE ON THEIR ASSIGNED RTE AND ALT. AFTER WE WERE CLR OF TFC WE ADVISED SVZM CTL OF THE INCIDENT AND ASKED WHAT ALT THEY WANTED US TO MAINTAIN. THEY INDICATED WE COULD STAY AT FL350. WE ASKED THEM 3 TIMES ABOUT OUR ALT AND THEY SEEMED INDIFFERENT AND HAD NO IDEA OF WHAT WAS GOING ON. AT THIS TIME FO EXPLAINED TO SVZM CTL IN SPANISH WHAT HAD HAPPENED AND THEY CLRED US TO FL330. EVEN AFTER BEING TOLD IN SPANISH; THEY DID NOT SEEM TO FEEL WHAT HAD HAPPENED WAS A PROB.