Narrative:

While cruising on an IFR flight plan at 16000 ft in VMC, ATC called traffic off my left wing at 15800 ft. Numerous turns and banking did not reveal the traffic and I could not make visual contact. I requested vectors to avoid traffic and I was given a 10 degree left turn. The traffic continued to be described as 'merged' by ATC at altitudes of 15500 ft to 16000 ft. After about 5-10 mins, I finally saw traffic in a descending left turn below, behind and to my left. It appeared to be a citation (cessna) with military markings. ATC claimed they were not 'working' the aircraft. I would suggest that military aircraft, when operating in the vicinity of GA, coordinate with ATC.

Google
 

Original NASA ASRS Text

Title: PLT OF AN SMA SEL ACFT ON AN IFR FLT PLAN, AND AT LEVEL CRUISING ALT, OBSERVED A MIL MLT ACFT DOING MANEUVERS WITHIN 1 MI OF HIS ACFT.

Narrative: WHILE CRUISING ON AN IFR FLT PLAN AT 16000 FT IN VMC, ATC CALLED TFC OFF MY L WING AT 15800 FT. NUMEROUS TURNS AND BANKING DID NOT REVEAL THE TFC AND I COULD NOT MAKE VISUAL CONTACT. I REQUESTED VECTORS TO AVOID TFC AND I WAS GIVEN A 10 DEG L TURN. THE TFC CONTINUED TO BE DESCRIBED AS 'MERGED' BY ATC AT ALTS OF 15500 FT TO 16000 FT. AFTER ABOUT 5-10 MINS, I FINALLY SAW TFC IN A DSNDING L TURN BELOW, BEHIND AND TO MY L. IT APPEARED TO BE A CITATION (CESSNA) WITH MIL MARKINGS. ATC CLAIMED THEY WERE NOT 'WORKING' THE ACFT. I WOULD SUGGEST THAT MIL ACFT, WHEN OPERATING IN THE VICINITY OF GA, COORDINATE WITH ATC.

Data retrieved from NASA's ASRS site as of July 2007 and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.