A GULFSTREAM 200 FLT CREW EXPERIENCED AN FMS MALFUNCTION AFTER DEP.

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ON JUL/FRI/03 TOOK OFF DAL AT XA24Z. THE DEP; DAL 7.SQS WAS ASSIGNED AND VERIFIED CORRECT IN THE FMS. GOOD INDICATIONS WERE VERIFIED FOR THE DEP AND ALL FLT PLAN FIXES WERE VERIFIED CORRECT. AFTER TKOF; WE WERE CLBING TO 5000 FT ON RWY HEADING. THEN CLBS TO 15000 FT; 17000 FT AND FL230 WERE ASSIGNED CONSECUTIVELY WITH THE CLRNC OF DIRECT SOLDO WITH A FREQ CHANGE. AFTER DIRECT SOLDO WAS SELECTED AND VERIFIED IN THE FMS; THE FMS; ON ITS OWN; DUMPED THE CURRENT FLT PLAN AND REPLACED IT WITH A FLT PLAN FROM JFK TO MIA. ON INITIAL CONTACT WITH THE NEXT CTLR WE REQUESTED A HDG TO SOLDO BECAUSE OF AN FMS MALFUNCTION. WE WERE ASSIGNED HEADING 090 DEGS AND TOLD TO CLB TO FL230 WE BEGAN NAV MANUALLY AND AT ATC'S REQUEST WE CHANGED OUR ACFT DESIGNATION. WHILE APCHING FL210 WE WERE INSTRUCTED TO STOP OUR CLB AT FL210 AND WE COMPLIED. LATER; WE WERE GIVEN ANOTHER HDG OF 100 DEGS AND POSSIBLY 110 DEGS. WE COMPLIED WITH EACH CLRNC GIVEN. EACH TIME WE PASSED A VOR WE ATTEMPTED TO RE-INITIALIZE THE FMS. EACH TIME THE FMS ACCEPTED THE INITIALIZATION FOR 5-10 SECONDS AND THEN REVERTED TO THE JFK AREA. XING THE NEXT VOR (THIRD ATTEMPT); WE AGAIN ATTEMPTED TO RE-INITIALIZE THE FMS. THIS TIME THE FMS ACCEPTED THE INITIALIZATION FOR THE REMAINDER OF THE FLT. DURING THE FLT; FORT WORTH APCH ASKED US TO CALL WHEN WE LANDED. WE NOTIFIED OUR PROGRAM MGR OF THE INCIDENT AND HE PHONED FOR US. AT NO TIME DURING THE FLT DID WE RECEIVE A TCASII TA OR RA.