AN ARTCC CTLR OBSERVES A KING AIR LOSE SEPARATION WITH AN MD88 IN HIS SECTOR AT ZME; TN.

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ACR; MD88; SEBOUND TO RMG; LNDG ATL. GA; BEECH KING AIR DEPARTED FROM BNA. KING AIR WAS CLBING TO FL280; MD88 LEVEL AT FL250. WHEN KING AIR OUT OF FL244; CONFLICT ALERT ACTIVATED. ACFT WERE APPROX 6 MI APART. MD88 ON MY FREQ; KING AIR ON R26 (JKS HI SECTOR) FREQ. I CALLED TFC TO MD88 AT 10 O'CLOCK POS; 3 MI AT FL250 (KING AIR MODE C). MD88 RESPONDED; 'I'LL GET BACK TO YOU;' AND EXECUTED TCASII RA. R26 DSNDED KING AIR TO FL240. TCASII ORDERED DSCNT ALSO; ON MD88. TARGETS MERGED AT SAME ALT. MD88 INFORMED ME OF TCASII RA AFTER RETURNING TO FL250. NO INJURIES. KING AIR WAS NOT TCASII EQUIPPED. SUPPLEMENTAL INFO FROM ACN 394079: LEVEL AT FL250 NOTED A TARGET ON TCASII AND THEN VISUALLY AT ABOUT 11 O'CLOCK POS; CO-ALT HEADED TOWARDS US. AS TARGET CAME INSIDE 10 NM A R TURN WAS INITIATED TO INSURE TARGET WOULD PASS BEHIND US. ANOTHER TARGET WAS ON TCASII AT FL240. AS R BANK BEGAN TCASII RA 'DSND' ANNUNCIATED WITH VSI GREEN ARC AT -3000 FPM. AUTOPLT WAS DISCONNECTED AND DSCNT INITIATED. AS THE TARGET AT FL250 PASSED ABOVE AND BEHIND; A 'CLB NOW' RA ANNUNCIATED BECAUSE OF THE TARGET AT FL240. A PULL UP WAS BEGUN AND 'CLR OF CONFLICT' ANNUNCIATED AS SOON AS DSCNT WAS ARRESTED AT FL245. THE CTLR WAS ADVISED OF THE RA AND SAID HE WAS NOT WORKING THE TFC AT OUR ALT. A TOTAL OF ABOUT 30-45 SECONDS ELAPSED FROM INITIAL SIGHTING TO 'CLR OF CONFLICT' ANNUNCIATION. AN EXPLANATION OF THE CO-ALT TFC WAS NOT GIVEN; BUT I FEEL IT WAS EITHER A MIL ACFT OR A CTLR HDOF PROB. THERE WAS HIGHER THAN NORMAL TFC VOLUME AT THE MID ALTS DUE TO TURB HIGHER. THE HEADS-UP PROVIDED BY THE TCASII DISPLAY PREVENTED A TOTAL SURPRISE WHEN THE RA ANNUNCIATED.