2 MIL F16 ACFT CONVERGE ON AN AIRLINER CAUSING AN NMAC AND A TCASII EVENT.

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INCREASE STAFFING AT ATC CTR TO ALLOW FOR ALL SECTORS TO BE OPENED AT BUSY TIMES. THE MIL PLT ADMITTED TO USING TERRAIN FOLLOWING EQUIP DURING THIS INCIDENT. THIS EQUIP PREVENTS HIM FROM USING ONBOARD RADAR AT THE SAME TIME. I WAS TRAINING CTLR ON THE R29 AND R30 SECTORS COMBINED. WE WERE MODERATELY BUSY WITH A COMBINATION OF CHARLOTTE ARRS/DEPS AND OVERFLTS. I OBSERVED 2 FAST MOVING VFR TARGETS NEAR PULASKI TRACKING SEBOUND. 1 TARGET SHOWED A MODE C OF 16500 FT AND THE OTHER 14500 FT. I ADVISED CTLR TO STOP ACFT X AT 17000 FT BECAUSE IT APPEARED THAT THEY MIGHT BE NEAR THE VFR. I ADVISED CTLR TO MAKE AN EARLY TFC CALL ON THE VFR BECAUSE OF ITS RAPID SPD. CTLR ISSUED TFC TO ACFT X WHEN THE TARGETS WERE 20 MI APART. I ADVISED CTLR TO ADVISE ACFT X THAT THE TFC WAS VERY FAST MOVING. CTLR ADVISED THE PLT THAT THE VFR WAS 'RAPIDLY MANEUVERING.' AT THIS POINT; THE VFR WAS NOT ON A DIRECT CONVERGING COURSE WITH ACFT X. I NOTICED THE VFR AT THE 1 O'CLOCK POS AND 7 MI FROM ACFT X. I THEN NOTICED THE VFR TURN DIRECTLY INTO THE ACR JET AND BEGIN CLBING. THE FREQ WAS CONGESTED DUE TO THE SECTORS BEING COMBINED AND I HAD TO WAIT A FEW SECONDS BEFORE ISSUING A SAFETY ADVISORY. WHEN THE FREQ CLRED; I ADVISED ACFT X 'TFC ALERT; TFC 12 O'CLOCK POS; 4 MI; OPPOSITE DIRECTION; 16800 FT AND CLBING.' ACFT X ANSWERED THAT THEY WERE RESPONDING TO AN RA AND CLBING. THE PLT OF ACFT X ADVISED ME THAT HE SAW THE MIL JET GO BY AND ONLY MISSED HIM BY 200 FT. I ADVISED MY SUPVR OF THE INCIDENT AND CONTINUED WORKING THE SECTORS.