THE RPTR SAW ANOTHER ACFT; POINTED OUT BY ARTCC; AND THOUGHT THAT HE WAS CLR ENOUGH TO CONTINUE HIS CLB. THE OTHER ACFT TOOK EVASIVE ACTION. THE RPTR SAID THAT IAD APCH HAD A NEAR MISS RPT FROM THE OTHER PLT.

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ON SATURDAY EVENING; OCT/SAT/1995 WHILE ENRTE FROM LOUISA COUNTY ARPT; VA (LKU); TO CALDWELL; NJ (CDW); I CONTACTED ZDC IN THE VICINITY OF BROOKE VOR. I MADE MY INITIAL CALL WHILE IN THE CLB TO 9500 FT REQUESTING ADVISORIES AND A TRANSITION THROUGH WASHINGTON'S CLASS B AIRSPACE AT 9500 FT; NEBOUND. CTR RESPONDED BY GIVING ME A SQUAWK CODE AND TELLING ME TO REMAIN CLR OF CLASS B AIRSPACE UNTIL RADAR IDENTED. UPON REACHING 9500 FT; I CALLED WASHINGTON TO SAY THAT I WOULD CONTINUE THE CLB TO 11500 FT. AROUND THIS TIME I WAS TOLD BY THE CTLR THAT HE HAD ME IN RADAR CONTACT AND THAT I HAD TFC ON MY R SIDE (1 OR 2 O'CLOCK) PASSING TO THE L. I RESPONDED BY SAYING I HAD THE TFC IN SIGHT. I THOUGHT THE TFC WAS NO FACTOR AND CONTINUED MY CLB TO 11500 FT. I WAS GIVEN NO INDICATION THAT THERE WAS ANY CONFLICT UNTIL; WHILE IN CONTACT WITH PHILADELPHIA APCH; I WAS GIVEN A TELEPHONE NUMBER AND ASKED TO PHONE DULLES APCH AFTER LNDG. UPON PHONING DULLES; I LEARNED THAT THE PLT OF THE OTHER ACFT CLAIMED THAT THERE WAS A NEAR MIDAIR COLLISION AND WANTED A RPT FILED. THE CTLR INFORMED ME THAT THE PLT OF THE OTHER ACFT CLAIMED THAT HE WAS AT 10000 FT AND HAD TO CLB TO 10500 FT AS I WAS AT 9800 FT. I ASSUME THAT THIS WAS A 'TCASII CLB.'