AN SF340 RECEIVES A TCASII RA WHILE FLYING CLOSE BY CBM AFB AS 2 T38 TRAINERS FLY DIRECTLY UNDERNEATH.

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WE WERE ENRTE FROM MGM TO MEM IN CRUISE FLT AT 6000 FT. WHEN ABOUT 20 MI NE OF COLUMBUS AFB; WE NOTICED TFC ON TCASII AT ABOUT 2 O'CLOCK. THE TFC WENT FROM WHITE TO YELLOW TO RED WITHIN A FEW SECONDS. WHEN THE TFC TURNED TO A SOLID WHITE DIAMOND WE STARTED LOOKING FOR THE TFC. THE ALT DISPLAY WAS CHANGING RAPIDLY AND THE TARGET WAS MOVING TOWARD US VERY FAST. SECONDS LATER I SAW A DASH 9 AND A YELLOW CIRCLE AND HEARD 'TFC; TFC.' ALMOST IMMEDIATELY I SAW A RED SQUARE WITH -3 AND HEARD A LOUD 'CLB; CLB.' I IMMEDIATELY INITIATED A CLB WITH MY FO DOING THE SAME. THE FO WAS LOOKING OUTSIDE AND SPOTTED 2 T38'S COMING TOWARD US IN FORMATION JUST AS WE GOT THE RA. THE RA WAS FOR A 2000 FPM CLB WHICH WE HELD UNTIL THE RA CLRED AT 7100 FT. THE FO SAID HE SAW 2 ACFT COME FROM ABOUT A 2:30 O'CLOCK POS TO ABOUT OUR 7 O'CLOCK POS PASSING UNDER US. I CALLED COLUMBUS APCH CTL AND TOLD THEM THAT WE HAD HAD AN RA AND WE WERE RETURNING TO OUR ASSIGNED ALT OF 6000 FT. I ASKED COLUMBUS APCH CTL ABOUT THE TFC AND THEY SAID 'YOUR TFC IS LEVEL AT 4000 FT.' I SAID; 'NO; THEY ARE NOT AT 4000 FT. THEY JUST PASSED WITHIN 300 FT VERTLY OF OUR ACFT.' COLUMBUS CAME BACK AND REPEATED THAT OUR TFC WAS LEVEL AT 4000 FT. I REPEATED; 'NO; THEY ARE NOT AT 4000 FT; THEY JUST PASSED WITHIN 300 FT VERTLY OF OUR ACFT.' OUR TCASII SHOWED THAT THEY CLBED VERY FAST AND WERE AT 5700 FT WHEN WE STARTED OUR CLB TO COMPLY WITH THE RA. WE WERE NEVER ADVISED BY COLUMBUS APCH CTL ABOUT THIS TFC.