ACR LGT HAD NEAR COLLISION WITH UNIDENTIFIED HIGH PERFORMANCE ACFT.

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ON ATC HDG OF 010 DEG DSNDING TO 6000'; CLR NIGHT 60 MI VISIBILITY. ACFT ABOVE US ABOUT 10-15 MI IN OUR 10 O'CLOCK POS CLOSING WITH RELATIVE POS REMAINING CONSTANT; ACFT DSNDED TO NEAR OUR ALT; CROSSED OVER US ABOUT 200' MAKING A 30 DEG PLUS ANGLE BANK TURN LEFT TO PARALLEL OUR COURSE. WE ASKED ATC IF THEY HAD ANY ACFT IN OUR POSITION-NEGATIVE. THE ACFT CONTINUED LEFT TURN TO PARALLEL OUR COURSE; WE TURNED SLIGHTLY TO LEFT AND CLBED ABOUT 1000' TO AVOID INCIDENT. THE OTHER ACFT FLEW FORMATION ON US FOR ABOUT 5-8 MI (OF RIGHT WING-100' STEP DOWN AND AFT) THEN SLOWED TO TRAIL US; ATC FINALLY ACQUIRED HIS RETURN (WE WERE MERGE PLOT) AS HE SLOWED FROM OUR 250 KT. NO FURTHER INCIDENT. LANDED AT IAD. PHONED IAD ATC. THEY WERE WORKING ON FINDING OUT WHO THE OTHER ACFT WAS. NOTE: ALL EXTERIOR LIGHTS WERE ON; LANDING LIGHTS; WING LIGHT TAIL 'LOGO' LIGHTS; ETC ANTI COLLISION. CALLBACK CONVERSATION REVEALED THE FOLLOWING INFO: THE CREW OF THE ACR LGT WERE NOT ABLE TO TELL THE TYPE OF OTHER ACFT; BUT FELT VERY STRONGLY THAT IT WAS A MIL HIGH-PERFORMANCE FGT. IT SEEMED TO BE TOYING WITH THIS ACR JET. WITH A SPEED OF 250 KTS; THE ACR CREW WATCHED THIS ACFT COME OVER THE TOP OF THEIR ACFT; MAKE A STEEP LEFT; DSNDING TURN AND COME UP ALONG SIDE THEIR ACFT AND THEN MOVE AHEAD AND DROP BACK BEHIND THEIR FLT. RPTR SAID THAT THEY NEVER FELT THERE WOULD BE A COLLISION; BUT THE ACTIONS OF THE OTHER ACFT CAUSED THEM APPREHENSION AT FIRST. DURING THE PHONE CALL TO ATC; IT WAS SPECULATED BY THE ATC THAT THE ACFT WAS A GENERAL AVIATION ACFT FROM MANASSAS ARPT; NEARBY BUT THE ACR FLT CREW REJECT THIS THEORY BASED ON THE SPEED OF THE OTHER ACFT. THE OTHER ACFT REMAINS A MYSTERY AIRPLANE.