ALTDEV ALT EXCURSION DURING TCASII RA.

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OUR ACFT; AN MLG; WAS IMC INBOUND TO DXO VOR ON THE STAR ARR INTO DTW KNOWN AS THE POLAR 1 ARR. DTW APCH HAD SLOWED US TO 210 KIAS AND INSTRUCTED US TO TURN TO 190 DEGS HDG AT TRAML INTXN. WE WERE 2 DME FROM TRAML (12 DME FROM DXO) WHEN TCASII ANNOUNCED 'TFC; TFC.' I NOTED A YELLOW GLOBE AT OUR 10 O'CLOCK BELOW US CLBING ON TCASII DISPLAY. TCASII THEN COMMANDED 'CLB; CLB; NOW.' THE IVSI SHOWED A RED ARC FROM -6000 FPM TO +1500 FPM AND GREEN ARC FROM +1500 TO +2000 FPM. THE FO WAS FLYING ON AUTOPLT ALT HOLD. I INSTRUCTED THE FO TO CLB AND; IN FACT; ASSISTED HIM BY DISCONNECTING THE AUTOPLT. HE CLBED THE ACFT INTO THE GREEN ARC; CLBING AT 1600 FPM. AT APPROX 11300 FT THE TCASII RED AND GREEN ARCS DISAPPEARED AND TCASII ANNOUNCED 'CLR OF CONFLICT.' THE 'ROUND OUT' GAVE US AN ALT OF 11500 MSL BEFORE DSNDING BACK DOWN TO 11000 MSL ASSIGNED. AT THE ONSET OF OUR TCASII COMMANDED CLB I NOTIFIED DTW APCH WE WERE IN A TCASII COMMANDED CLB. THE DTW APCH CTLR SAID THERE WAS IN FACT TFC CLBING OUT OF DTW BELOW US. I CANNOT AND DO NOT RECALL SEEING THE YELLOW TCASII SYMBOL DEPICTION ANY CLOSER THAN 900 FT.