A B757-200 FO RPT ON A NEAR NMAC WITH OPPOSITE DIRECTION TFC 500 FT ABOVE; TCASII IDENTED; BUT NOT ON APCH CTLR'S RADAR AT CVG; OH.

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WHILE UNDER CTL OF CVG APCH; LEVEL AT 11000 FT; JUST NW OF FLM VORTAC AT NIGHT; WE SUDDENLY GOT A TA FOLLOWED VERY QUICKLY BY AN RA. WE BOTH SAW TA FOLLOWED BY RA ON THE CTR RADAR/TCASII CRT. NO CLB OR DSCNT NOTED FROM TFC; HDG SE AT 11500 FT. WE QUICKLY VISUALLY SAW ACFT ABOVE AND AHEAD. RA SAID TO DSND. I TOLD CVG APCH ABOUT RA. THEY SAID THAT THEY DID NOT HAVE ANY TFC ON RADAR NEAR US. I AGAIN SAID WHAT WE SAW ON TCASII VISUALLY. RA CHANGED TO TA AS PLANE WENT OVER US AND SUBSEQUENTLY CHANGED TO 'NON CONFLICT' TFC. CVG APCH THEN STATED THEY COULD SEE A 'PRIMARY TARGET.' THEY THEN PASSED OUR 11500 FT RPT TO OTHERS BEHIND US ON THE ARR. THE UNIDENTED ACFT WAS GOING SE ON V517 -- PROPER DIRECTION/ALT FOR VFR. TOP OF CVG CLASS B AIRSPACE IS 8000 FT. DID UNIDENTED ACFT HAVE VERY WEAK XPONDER? WAS ITS ANTENNA 'AIMED' FORWARD? IE; ANTENNA HIDDEN FROM 'AFT' RADAR SITE? PERHAPS APCH SHOULD USE 12000 FT OR 10000 FT INSTEAD OF 'WRONG WAY' 11000 FT? WAS/WERE ONE OR BOTH XPONDERS WORKING IMPROPERLY?