MD88 FLT CREW INITIATE TCASII MANEUVER AT FL240 TO EVADE A DSNDING C550. C550 IN EMER DSCNT. NO ZTL TFC EXCHANGE.

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WE WERE CRUISING AT FL240 WITH A CLRNC TO FLY DIRECT TO ODF VOR. THE TCASII SYS GAVE AN AURAL 'TFC' ALERT AND DISPLAYED A TARGET AT 11 O'CLOCK POS AND 6-7 NM AWAY; APPROX 4500 FT ABOVE. WE BOTH ACQUIRED THE TFC VISUALLY AND THE CAPT ATTEMPTED TO CALL ATC ABOUT IT. BEFORE ATC REPLIED; TCASII CHANGED TO AN RA WITH GUIDANCE TO CLB. THE CAPT INITIATED A CLB AND A SLIGHT R TURN TO AVOID THE OTHER ACFT. THE OTHER ACFT DID NOT APPEAR TO ALTER ITS FLT PATH; AND IT PASSED THROUGH OUR ALT AND SLIGHTLY TO OUR L (LESS THAN 500 FT AWAY). WE RPTED OUR CLB TO ATC AND WERE RECLRED TO FL240 'WHEN ABLE.' ATC IDENTED THE OTHER ACFT AS A CITATION 550; AND SAID THEY WERE ON AN EMER DSCNT DUE TO PRESSURIZATION PROBS. LATER; BY PHONE; ATC INFORMED THE CAPT THAT THE CITATION HAD BEEN CRUISING AT FL410 PRIOR TO THE INCIDENT AND HAD BEEN ASKED DURING THE INCIDENT TO LEVELOFF AT FL250. OPINIONS: 1) ATC SHOULD NOT ASK AN EMER ACFT TO LEVEL OFF IN ORDER TO PROVIDE SEPARATION. 2) ATC HAD PLENTY OF TIME TO RECOGNIZE THE POTENTIAL CONFLICT AND SHOULD HAVE ISSUED VECTORS TO US TO RESOLVE THE CONFLICT. 3) TCASII SAVED THE DAY! THIS WOULD HAVE BEEN A COLLISION! SUPPLEMENTAL INFO FROM ACN 576329: WE DID TRY TO CALL CTLR; BUT COULD NOT GET THROUGH. ATC HAD AT LEAST 2-3 MINS TO SEE THE CONFLICT AND MOVE US BUT DID NOTHING. WITHOUT THE TCASII TO GIVE US THE HEADS UP; WE NEVER WOULD HAVE SEEN THE SMALLER CITATION DSNDING AT A HIGH RATE ON TOP OF US.