ACR INBOUND TO DCA EXPERIENCES LOSS OF FMC'S AND DEVIATES OFF COURSE. CTLR CATCHES ERROR.

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ON OUR THIRD LEG OF OUR DAILY TRIP WE WERE APCHING BILIT INTXN (BOS TO DCA) ENRTE TO DCA. JUST PRIOR TO BILIT INTXN BOTH OUR FMC'S BLANKED AND FINALLY RECOVERED. OUR ROUTING/CLRNC WAS TO GO FROM BILIT TO DCA. ON TOP OF OUR FMC'S GOING INOP; THE ACFT BEGAN TO SLOWLY DSND UNCOMMANDED OUT OF OUR SELECTED ALT. I WAS FLYING THE ACFT AND HAD TO DISCONNECT THE ACFT FROM THE AUTOPLT AND MANUALLY FLY THE ACFT UNTIL WE COULD GET THE COMPUTERS BACK UP. AT THE SAME TIME THE DCA/WASHINGTON CTLR ASKED US WHAT OUR ROUTING WAS AND I ASKED HIM WHAT HE WANTED AND HE STATED THAT WE WERE SUPPOSED TO BE GOING TO DCA DIRECTLY. BOTH THE CAPT AND I FELT THAT WE WERE HEADED TO DCA DIRECTLY; BUT FOLLOWING THE FMC FAILURE; THE COMPUTER WAS COMMANDING THE AUTOPLT TO STEER SLIGHTLY OFF COURSE TO AN UNKNOWN POINT. WE AGAIN SELECTED DCA DIRECT AND THERE WAS A SLIGHT TURN. THE CTLR STATED THAT THIS AREA BTWN BILIT AND DCA HAS MANY RTE DEVS FROM ALL AIRLINES ON THIS SEGMENT. OUR TCASII HAD NO ACFT IN THE LCL AREA AT ANY ALT AT THE TIME OF THIS EVENT. IT DID NOT APPEAR THAT WE WERE OFF COURSE THAT MUCH IF ANY; BUT THE CTLR ACTED CONCERNED. THROUGHOUT THIS LEG WE HAD BEEN REQUESTED BY BOS; NY; AND WASHINGTON CTLRS TO CARRY OUT MANY HDG; ALT AND AIRSPD CHANGES THROUGHOUT THIS 1:39 HR FLT WHICH DEMANDED AN ABNORMAL AMOUNT OF ATTN. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO. RPTR STATES THAT THEY WERE ABOUT 30 MI E OF ARPT WHEN INCIDENT OCCURRED. RPTR IS NEW TO THIS ACFT; HAS ONLY BEEN FLYING IT FOR ABOUT 4 WKS. HOWEVER; HE HAS A LOT OF EXPERIENCE IN GLASS COCKPIT ACFT. HE SAID THAT FMC PROBLEMS ARE NOT NEW THESE ACFT. DOES NOT KNOW WHAT THE PROBLEMS ARE. HE MENTIONED THAT AROUND THIS TIME THEIR MAINT PEOPLE WERE HAVING A LABOR DISPUTE AND ALLEGEDLY; SOME HAD EMPTIED ALL INFO FROM THE FMC. THIS LASTED FOR ABOUT 1 WK. THE CTLR MENTIONED TO THEM THAT THERE HAVE BEEN MANY ACFT OFF COURSE APPARENTLY REFERRING TO EITHER FMC PROBLEMS OF FLCS NOT PAYING ATTN.