B767ER SUFFERS DEGRADED FMS NAV POSITIONING GUIDANCE FOLLOWING ATLANTIC CROSSING.

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UPON EXITING THE NORTH ATLANTIC TRACK SYS AND COMING INTO RADAR AND VHF CONTACT WITH MONTREAL CTR; WE WERE ASKED TO VERIFY POS. WE WERE APPROX 10 NM E OF LAKES INTXN. MONTREAL HAD OUR POS FURTHER S. THEIR POS DID NOT AGREE WITH EITHER OUR FMC OR IRS POS. RADAR VECTORS WERE PROVIDED UNTIL WE WERE ABLE TO RECEIVE LAND BASED RADIO NAVAID SIGNALS. CTR WAS ADVISED THAT OUR RNAV CAPABILITY WAS UNRELIABLE AND THE REMAINING PORTION OF THE FLT WAS FLOWN USING MANUAL RADIO NAVAID TUNING. THE ACFT POS WAS INITIALIZED AND VERIFIED AT THE GATE IN FRANKFURT AND AN RNAV DEP WAS FLOWN. AT NO TIME DID ANY CTLING AGENCY QUESTION OUR POS. PRIOR TO ENTERING THE TRACKS A NAV ACCURACY CHK WAS PERFORMED AND RAW DATA AND FMC DATA WERE WITHIN TOLERANCE. THERE WAS ALSO ANOTHER ACFT ENTERING THE TRACKS AT THE SAME TIME AND POS 1000 FT BELOW US. NEITHER OUR POS NOR HIS WAS QUESTIONED BY SHANNON CTL. ONCE ACROSS THE TRACKS AND IN RANGE OF RADIO NAVAIDS IT SEEMED AS IF THE FMC WAS NOT UPDATING ITS POS AS FREQUENT NAV ACCURACY CHKS SHOWED RAW DATA VERSUS FMC TO BE OUT OF LIMITS. THE FMC SYS WAS WRITTEN UP IN THE MAINT LOG AS BEING UNRELIABLE.