LEAR LR60 FLT CREW HAS A TRACK AND OR HDG DEV DURING OCEANIC TRANSIT.

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WE TOOK OFF FROM BERMUDA (TXKF) IN A LEAR 60. AT CRUISE FL380 WE MADE OUR NORMAL POS RPTS. THE ONLY THING THAT STUCK OUT WAS MIDWAY THROUGH THE FLT THE WIND DIRECTION AND READOUT OF ABOUT 90 KT HEADWIND WAS NO LONGER VISIBLE; ON THE MFD (MULTI-FUNCTION DISPLAY). WE THOUGHT IT WAS ODD THAT THE WIND WENT CALM ALL OF A SUDDEN. NEW YORK OCEANIC GAVE US A FREQ TO CONTACT MIAMI 5 MINS OUTSIDE SUMRS INTXN. THE OTHER THING THAT CAUGHT OUR ATTN WAS WHEN NEW YORK OCEANIC ASKED US SEVERAL TIMES TO VERIFY OUR TIMES AND SPD. 5 MINS OUTSIDE OF SUMRS INTXN AND THEN AGAIN OVER SUMRS INTXN; WE COULD NOT RAISE ZMA EXCEPT THROUGH ANOTHER ACFT RELAY. WHEN OUR ACFT FMS TOLD US WE WERE OVER NUCAR MIAMI ADVISED US THAT IF WE WERE OVER NUCAR THEY WOULD BE ABLE TO SEE US ON RADAR. WE THEN KNEW SOMETHING WAS WRONG. THEN MIAMI SAID THEY HAD US A LITTLE WHILE LATER BUT 10 MI OUTSIDE NUCAR. WE REINITIALIZED OUR #2 FMS INFLT AND HAD NO OTHER DEV. IT SEEMS TO ME THE WIND READOUT WAS NO LONGER COMPENSATING FOR THE HEADWIND PUTTING THE ACFT FARTHER BEHIND THEN IT WAS SHOWING ON THE MFD.