L1011 FLC RECEIVES A TCASII TA THEN RA THEN APCH CTL ALERT TO CLB. OTHER ACFT SUPPOSED TO BE MAINTAINING VISUAL SEPARATION.

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DSNDING INTO ATL IN CLR AND VFR CONDITIONS; THE FO WAS FLYING. WE WERE ON VECTORS FOR THE ILS RWY 8L WHEN WE FIRST RECEIVED A TA ON THE TCASII AT ABOUT 7500 FT MSL; FOLLOWED QUICKLY BY AN RA AND SIMULTANEOUSLY BY APCH CTL TELLING US TO MAKE AN IMMEDIATE CLB TO 7500 FT FOR A DC9 AT 7000 FT WHO WAS SUPPOSED TO BE MAINTAINING VISUAL SEPARATION FROM US. THE TCASII SAID ONE TIME; 'DSND' AND THEN WENT TO 'CLB.' WE TOOK AGGRESSIVE ACTION BUT LOST SIGHT OF THE DC9 AS WE CLBED BACK TO 7500 FT. I BELIEVE SOME FACTORS INVOLVED THAT SLOWED MY RESPONSE WERE THE DC9 WAS MIL (NO TCASII). WHEN THE TCASII SOUNDED 'DSND;' I EXPECTED THE DC9 TO CLB; BUT WITH NO TCASII; HE RECEIVED NO COMMANDS. ADDITIONALLY; HIS POS RELATIVE TO THE ATLANTA ARPT WAS INCONSISTENT WITH NORMAL ARRS TO THE ATL ARPT IN THAT HE WAS LEVEL AT 7000 FT N OF WHERE HE SHOULD HAVE BEEN AND HDG N. I LEARNED LATER HE WAS GOING TO DOBBINS AFB ON AN ARR FOR THAT ARPT; BUT I WAS NOT EXPECTING HIM IN THAT POS AND THERE WAS NO COM FROM APCH CTL ABOUT HIM UNTIL WE WERE TOLD TO CLB TO 7500 FT.