A B747-400 PIC IS ADVISED BY RUSSIAN RADAR CTLR THAT HE IS 3-6 MI R OF THE CTRLINE OF AIRWAY G212; XR; FO.

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ON RUSSIAN AIRWAY G212 OVER XR; CTLR SAID WE WERE 5 KM R OF COURSE. SHORTLY THEREAFTER; HE SAID 10 KM R OF COURSE. MY FO AND I CHKED ALL WE COULD AND WE REPLIED WE WERE ON COURSE. THE NEXT CHK POINT CTLR SAID 5 KM R OF COURSE. WE TUNED ALL NDB'S AND WATCHED ANOTHER ACFT ON TCASII ABOUT 4 MI L OF US. I NOTICED THE NDB AT THE NEXT FIX L OF US. I DECIDED TO FLY A L 2 NM OFFSET. ABOUT 1 HR LATER; I FLEW 3 NM L OFFSET FOR THE REMAINDER OF RUSSIAN AIRSPACE BECAUSE OTHER ACFT WERE STILL 1 OR 2 MI L OF US; AND NDB STILL SHOWED US SLIGHTLY R OF COURSE. WHEN CALLING ZAN OVER FRENK; WE HAD SOME DME UPDATING ON THE FMC'S. PRIOR TO THIS; 'IRS ONLY' WAS OUR NAV. I DELETED THE L 3 NM OFFSET NEAR FRENK; AND ZAN SHOWED US ON COURSE IN ZAN. WITH NO DME UPDATING OF FMC'S I SHOULD HAVE DECLARED 'NAV SYS UNRELIABLE' TO ATC. I HAVE BECOME TOO CONFIDENT IN THE NAV SYS OVER YRS OF ACCURACY. I DO NOT KNOW WHY RUSSIAN ATC SAID 5 KM AND THEN 10 KM SHORTLY AFTER -- MAYBE TO GET OUR ATTN BETTER. WE ASKED RUSSIAN ATC AFTER XR AND FLYING L OFFSET IF WE WERE ON COURSE. THEY NEVER HAD A PROB WITH OUR COURSE AFTER THAT. THE L OFFSET CORRECTED THE COURSE; BUT I SHOULD HAVE SAID 'NAV SYS UNRELIABLE.'