NMAC OVER CENTRAL AMERICA BTWN A LR25 CLBING TO ASSIGNED ALT AND AN ACR IN CRUISE AT NIGHT.

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WX: VMC. NBOUND ON UG765 BTWN TILOT AND NANDO INTXNS (S OF CTM VOR) UNDER CENTAMER CTL (NON-RADAR). ORIGINAL CLRNC WAS DIRECT CLB TO FL370. LATER AMENDED TO FL290. APCHING FL290 WE REQUESTED AND WERE CLRED TO FL410. CENTAMER CTL REQUESTED THAT WE EXPEDITE CLB TO FL410. DURING THE CLB; CENTAMER CTL MADE REPEATED INQUIRIES AS TO OUR FLT LEVEL. WE RESPONDED PROMPTLY AND ACCURATELY TO THESE INQUIRIES. NO MENTION WAS EVER MADE OF ANY POSSIBLE TFC CONFLICT. AFTER LEVELING AT FL410 THE CARGO HANDLER AND TRANSLATOR OVERHEARD AN EXTENSIVE CONVERSATION GOING ON OVER CTR FREQ IN SPANISH BTWN CENTAMER CTL AND ACR Y FLT. ACR Y WAS INQUIRING AS TO ANOTHER ACFT'S (US?) ALT; POS; AND REGISTRATION NUMBER. AFTER OVERHEARING THE CTLR GIVE OUT OUR 'N' NUMBER TO THE ACR Y CREW; INQUIRED TO THE CTLR (IN ENGLISH) AS TO WHAT THE CONVERSATION IN SPANISH WAS ABOUT. THE ACR Y CREW CAME BACK AND CLAIMED THAT THEY HAD HAD A NEAR MISS WITH US AS WE CLBED THROUGH FL370 AND THEY WERE OPPOSITE DIRECTION; LEVEL AT FL370. WE NEVER HAD VISUAL CONTACT WITH THIS TFC; NOR WERE WE ALERTED TO HIS PRESENCE BY CENTAMER CTL. AT NO TIME WERE WE EVER GIVEN ANY INDICATION FROM CENTAMER CTL THAT THE TFC EXISTED; LET ALONE HIS RELATIVE POS OR RELEVANCE TO OUR FLT PATH. IF IT HAD NOT BEEN FOR HAVING A BILINGUAL PERSON ONBOARD THE ACFT WE NEVER WOULD HAVE HAD ANY INDICATION THAT ANYTHING UNUSUAL HAD TRANSPIRED. SINCE THERE WAS OPPOSING TFC AT FL370; WHY DIDN'T CENTAMER STOP OUR CLB AT FL350. WHY WERE WE NOT ALERTED AT ANY TIME TO THE OPPOSING TFC'S PRESENCE?