A B767-200 FMS DID NOT PERFORM VOR UPDATES AFTER TKOF AND DEVIATED 15 NM FROM TRACK BEFORE RETURNING TO LAND.

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BOTH PLTS VERIFIED RTE AND GATE POSITION. PRIOR TO TAKEOFF RWY ALIGNMENT WAS VERIFIED. DEP CTL CLRED US DIRECT TO INTXN. FMC SHOWED US ON COURSE; HOWEVER; DEP CTL INFORMED US WE WERE 60 DEGS OFF AND GAVE US A HEADING TO INTERCEPT THE AIRWAY S OF VOR. AGAIN FMC SHOWED US ON COURSE. IN LIGHT OF OUR PREVIOUS EXPERIENCE; WE ELECTED TO VERIFY THE FMC'S WITH VOR'S AND DISCOVERED THE FMC'S WERE AT LEAST 15 MILES OFF. FMC'S WOULD NOT UPDATE OFF VOR'S. I ELECTED TO RETURN TO ZZZ. I DON'T KNOW WHAT CAUSED THE FAILURE; HOWEVER; MAINT WAS STILL WORKING ON IT 9 HRS LATER. HAD FAILURE OCCURRED IN MOUNTAINOUS TERRAIN IN IMC; THE RESULTS COULD HAVE BEEN DISASTROUS. AS A RESULT; I PHONED THE BASE CHIEF PLTS OFFICE AND REQUESTED THE POST REPAIR CREW BE GIVEN A 'HEADS UP;' AS TO OUR EXPERIENCE IN ORDER THEY WATCH FMC PERFORMANCE CAREFULLY.SUPPLEMENTAL INFO FROM ACN 761191: ON CLIMB-OUT; DEP CLRED US TO INTXN. AS THE NON-FLYING PLT I SELECTED DIRECT INTXN; VERIFIED IT WITH THE CAPT AND EXECUTED IT. AT THE CAPT'S CALL I ENGAGED L-NAV. DEP ASKED US TO VERIFY DIRECT INTXN WHICH I DID AND THEN PROCEEDED TO VERIFY IT OFF OF THE VOR. IT LOOKED CLOSE BUT I COULDN'T SAY INITIALLY THAT IT WAS PERFECTLY ACCURATE. WE WERE THEN GIVEN A HEADING TO HOLD AND I TOLD THE CTLR THAT I QUESTIONED OUR NAV SYSTEM ACCURACY. WE SWITCHED TO ANOTHER CTR AND WERE CLRED DIRECT TO VOR. I DIALED IN THE VOR FREQ AND WE PROCEEDED UTILIZING VOR NAV. WE THEN RECEIVED A FMS MESSAGE-PURGE UPDATE POS 2; FOLLOWED BY IRS NAV ONLY. THE CAPT ACARS DISPATCH AND THEN DECIDED TO RETURN TO ZZZ. WE MADE AN OVERWT LNDG; REASONING THAT IT WAS MORE PRUDENT THAN CIRCLING TO BURN DOWN TO LNDG WT.CALLBACK CONVERSATION WITH RPTR ACN 762140 REVEALED THE FOLLOWING INFO: THE RPTR EMPHASIZED THAT THE CREW PERFORMED THE PREFLT ALIGNMENT PROPERLY AND DID NOT GET THE FLASHING ALIGN LIGHTS INDICATING A POSITION ERROR. ON TKOF A RWY ALIGNMENT WAS COMPLETED WITH NO ERROR INDICATED. HOWEVER VERY SHORTLY AFTER TKOF A NAV ERROR DEVELOPED. WHILE TROUBLESHOOTING; THE RPTR STATED THAT NO VOR STATIONS WERE IDENTIFIED ON THE PROGRESS PAGE TO INDICATE THEIR USAGE FOR CONTINUOUS FMS POSITION UPDATE. THERE WAS NEVER AN ERROR MSG INDICATING A PROBLEM MUCH LESS WHAT TYPE OF PROBLEM. UPON RETURN TO THE DEP ARPT; MAINT TOOK THE ACFT AND WHEN THE RPTR CHECKED WITH THEM 12 HOURS LATER; NO CAUSE HAD BEEN IDENTIFIED. THE RPTR IS CONCERNED ABOUT THIS ACFT BEING FLOWN WHERE TERRAIN IS AN ISSUE. OVERALL THE RPTR FEELS THIS ACFT'S PROBLEMS MAY FIT INTO THE AGING ACFT CATEGORY.