A B727-200 CARGO HAULER IS NOTIFIED BY ZME CTLR THAT THEY ARE 3 MI S OF THE 045 DEG RADIAL OF MEM; TN.

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AT FL310 ON A FLT INBOUND TO MEM FROM THE NE; ZME GAVE US A VECTOR OFF THE STAR (ARR RTE) IN THE FORM OF A HDG IN WHICH TO INTERCEPT THE MEM 045 DEG RADIAL (225 DEG COURSE) INBOUND TO THE VOR. JUST AS WE WERE TURNING TO INTERCEPT THE COURSE; ATC ASKED US TO CONFIRM THAT WE WERE TURNING TO JOIN THE RADIAL (045 DEGS). WE ACKNOWLEDGED YES AND WERE GIVEN A FREQ CHANGE. A FEW MINS AFTER WE HAD CHKED IN WITH THE NEXT SECTOR; THE CTLR ASKED US IF WE HAD BEEN GIVEN A HDG TO JOIN THE 045 DEG RADIAL. WE RESPONDED THAT THE PREVIOUS CTLR HAD GIVEN US A HDG BUT THAT NOW WE WERE ESTABLISHED ON COURSE (WITH OUR VOR NAV INDICATING INSTS) TRACKING THE CTRLINE OF THE RADIAL. WE ASKED THE CTLR IF HE SHOWED US ON COURSE. THE CTLR SAID HE SHOWED US 4 MI S OF COURSE. AGAIN WE TOLD HIM THAT WE WERE ESTABLISHED ON COURSE TRACKING THE CTRLINE. AFTER ANOTHER FREQ CHANGE; WE NOTICED THAT THE CAPT'S (WHO WAS FLYING) VOR NAV NEEDLE WAS INDICATING CTRED AND THE FO'S WAS INDICATING SLIGHTLY (LESS THAN 3 DEGS) OFF COURSE TO THE S (RADIAL WAS TO THE N). WE CONCLUDED THAT THE FO'S VOR NAV INST WAS A LITTLE MORE ACCURATE THAN THE CAPT'S. THE REMAINDER OF THE FLT WAS UNEVENTFUL. WHAT I BELIEVE CAUSED THIS ERROR TO DEVELOP WAS NOT ACCURATELY XCHKING BOTH NAV INSTS FOR ANY DEVS. ALSO FLYING OFF 1 VOR INDICATION ONLY AND NOT TRYING TO KEEP BOTH VOR INDICATIONS CTRED IN YOUR SCAN JUST IN CASE ONE IS NOT AS ACCURATE AS THE OTHER ONE.