FLT CREW PROGRAMMED THE FMC USING THE ON BOARD STORED FLT PLAN. CLRNC WAS FOR A DIFFERENT PLANNED ROUTE. ARTCC CTLR ADVISED FLT OPERATING ON THE WRONG AIRWAY; WAS 60 MILES OFF COURSE AND CAUSED LESS THAN STANDARD SEPARATION WITH ANOTHER ACFT.

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ON A STOPOVER IN CANCUN; MEXICO; I PREFLTED THE FMC; ENTERED CUN ATL IN COMPANY ROUTE AND THE COMPANY ROUTE READOUT (DIRECT ROBIN; UA321 PLADE; R875; 45 MID; ETC). I ALSO SET UP THE VHF NAV FOR DIRECT ROBIN INTXN AS A BACKUP TO THE LAT NAV. DEPARTED CANCUN TO NW; TURNED ON COURSE 011 DEG R TOWARDS ROBIN INTXN. CLRNC FROM CANCUN TWR READ; 'AS FILED TO MAINTAIN FL350 DEP FREQ SQUAWK 1034.' AT APPROX 60 MI FROM CANCUN AND PASSING FL260 FOR FL350; MERIDA CENTER ADVISED US THAT WE WERE OFF COURSE AND APPEARED TO BE ON THE WRONG ARWY. THEY ALSO ADVISED US THAT WE CAME 'VERY CLOSE' TO ANOTHER ACFT. I LOOKED AT OUR FLT PLAN ON THE PAPERWORK AND IT READ: CUN A26E PARRA UA26 SWORD A26 GNI MEI LGCG ATL. WE WERE INDEED FLYING THE WRONG ARWY. THE CAPT AND MYSELF FAILED TO VERIFY THE CLRNC WITH CANCUN TWR BEFORE OUR DEP; NOR EVEN TO XCHK OUR COMPUTER STOWED FLT PLAN WITH THE PAPERWORK FROM FILED FLT PLAN. I; NOR THE CAPT; DID NOT OBSERVE ANY CONFLICT IN TFC; NOR DID WE HEAR ANY COMPLAINTS ON FREQ ABOUT A NEAR MISS. THERE WAS NO MENTION OF HOW CLOSE WE CAME. THE CAPT WAS A CHK AIRMAN ON THE MLG WITH MANY YRS EXPERIENCE. I; AS THE F/O; HAD 4 YRS FLYING MLG; 1500 HRS AS PIC ON MLG. PERHAPS WE RELIED TOO MUCH ON EACH OTHER TO DO THE JOB PROPERLY AND THAT LITTLE OVERLOOKED ASSUMPTION THAT THE BOX WOULD NEVER LIE CAUGHT UP WITH US.