DC9 EXPERIENCED TCASII RA DURING DSCNT INTO ORD NEAR FL250 WITH ANOTHER ACR DUE TO AN ALT OVERSHOOT.

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WHILE CRUISING AT FL290; WE WERE INSTRUCTED TO DSND TO FL240 BY ZAU. WE ACKNOWLEDGED AND BEGAN A DSCNT TO FL240. PASSING FL280; CTR ASKED US TO EXPEDITE TO FL240. WE ACKNOWLEDGED AND INCREASED DSCNT RATE. WE HEARD AN ACR Y JET BEING GIVEN DSCNT INSTRUCTIONS ALSO. ZAU ASKED US TO BE BELOW FL250 IN 1 MIN OR LESS (WE WERE AT FL265). WE ACKNOWLEDGED AND INCREASED DSCNT RATE TO 2000-2500 FPM. ZAU ASKED ACR Y FLT HIS ALT. HE SAID 'FL240.' ZAU SAID HE WAS ONLY CLRED TO FL260. ACR Y SAID 'HE PUT THE WRONG THING IN THE WINDOW.' ZAU TOLD ACR Y TO DSND IMMEDIATELY TO FL230. AT THIS TIME WE HAD A VISUAL ON ACR Y FLT AT OUR 11-12 O'CLOCK POS. I HAD STOPPED DSNDING AT FL245 AND BEGAN MANEUVERING TO AVOID ACR Y. TCASII GAVE US AN RA TO 'DSND.' BECAUSE OF VISUAL WITH ACR Y BELOW US; WE CLBED AND TURNED AT 10-15 DEGS L. CTR THEN ASKED US IF WE WERE AT FL250. WE SAID 'NO; WE NEVER HEARD INSTRUCTIONS TO CLB TO FL250 BUT; WE COULD CLB THERE.' THEY; (ZAU) SAID; 'NO; DSND TO BE AT FL230 AT GEIBER INTXN.' OUR TCASII GAVE US 'CLR OF CONFLICT.'