TCASII RA ACTIVATE AS AUTOPLT ALT. HOLD DEVS PLUS OR MINUS 200 FT. WHILE IN HOLDING PATTERN.

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ENTERED HOLDING AT SIOUX FALLS (FSO) W ON 270 RADIAL AT FL240. AUTOPLT WAS ENGAGED IN MANUAL MODE; WITH ALT HOLD SELECTED AND WITH THE AUTO THROTTLES ENGAGED IN THE SPD MODE. AN ACR Y MD-80 ALSO ENTERED HOLDING AT THE SAME TIME AND LOCATION AT FL280. I FLEW A TEARDROP ENTRY WITH A HDG OF 240 DEGS FOR 1 1/2 MINS AND THEN MADE A R HAND TURN TO INTERCEPT 270 RADIAL INBOUND TOWARDS SIOUX FALLS VORTAC. AT XP01 OVERHEAD FSD VORTAC I STARTED A R HAND TURN TO A HDG OF 270 DEGS. DURING THE TURN I NOTICED AUTOPLT STARTED TO SLOWLY CLB EVEN THOUGH ALT HOLD WAS SELECTED. AT 29150 I DISENGAGED ALT HOLD AND STARTED A DSCNT BACK TO FL290. I DSNDED TO FL28.9 AND WAS STARTING TO CORRECT BACK TOWARDS FL290 WHEN THE TCASII RA CAME ON COMMANDING A CLB. I FOLLOWED TCASII ADVISORY; CLRED AIRSPACE ABOVE AND PROMPTLY STARTED A SMOOTH CLB TO TRY TO DEEP VSI NEEDLE JUST OUTSIDE THE RED AREA ON THE VSI. PASSING FL29.1 WE RECEIVED CLR OF CONFLICT AND AT FL29.2 I PROMPTLY AND SMOOTHLY RETURNED ACFT BACK TO FL290. WHEN WE HEARD CLR OF CONFLICT SO SIGHTED AN ACR Y MD-80 IN A R-HAND TURN BELOW US AT THE 3 O'CLOCK POS. IT LOOKED TO ME TO BE AT 1000 FT BELOW. CAPT ADVISED ZMP THAT A SIT OCCURRED WHICH CAUSES A TCASII RA AT XB03Z ZMP CONFIRMED THAT BOTH ACFT WERE AT THE PROPER ALTS.