B737-300 CREW FORCED AN AUTOPLT TO ENGAGE. THEY HAD AN ALTDEV WHEN IT DISCONNECTED; AND THE ACFT WAS NOT IN TRIM.

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ON CLBOUT; CAPT (PF) INITIALLY HAD TROUBLE ENGAGING AUTOPLT #1. AUTOPLT #2 WAS ENGAGED AND USED FOR A SHORT PERIOD OF TIME; FOLLOWED BY #1 AUTOPLT FINALLY BEING ENGAGED AND USED. AT FL310; ACFT BEGAN TO LEVEL OFF; AND THE FMA PITCH WINDOW READ 'ALT ACQUIRED.' I TOLD CAPT I'D BE OFF FREQ TO CALL COMPANY ON #2 RADIO TO CHK OUR 'OUT' AND 'OFF' TIMES. ACARS CLOCK WAS INCORRECT. THE AUTOPLT AURAL WARNING (DISCONNECTED) GOT MY ATTN. I LOOKED UP; AND ACFT WAS CLBING THROUGH FL315; AND CAPT HAD BOTH HANDS ON CTL YOKE PUSHING FORWARD. HE GOT THE CLB STOPPED AT ABOUT FL317; AND DSNDED BACK TO FL310. ATC SAID NOTHING AS WE TRIED TO FIGURE OUT WHAT JUST HAPPENED. EARLIER IN THE FLT; WHEN THE CAPT HAD TROUBLE ENGAGING AUTOPLT #1; THERE WERE SEVERAL TIMES THE STABILIZER OUT OF TRIM LIGHT CAME ON. ALSO; AFTER THE INCIDENT; AND BACK TO LEVEL FLT; THE CAPT RE-ENGAGED AUTOPLT; AND IT WOULD NOT HOLD ALT. THAT WAS ABOUT THE TIME I TOLD THE CAPT THAT I DIDN'T THINK THE AUTOPLT TRIM WAS WORKING; AS THE TRIM WHEEL WAS NOT MOVING WHEN THE AUTOPLT WAS ENGAGED. WE FOUND A CIRCUIT BREAKER TRIPPED. AFTER SEVERAL MINS OF DISCUSSION; WE AGREED IT WOULD BE OK TO RESET CIRCUIT BREAKER AND CHK THE AUTOPLT AGAIN. WE DID; AND AUTOPLT OPERATED PROPERLY. DURING LNDG CHKLIST 'RECALL-CHKED' MASTER CAUTION AND SPD TRIM FAIL LIGHTS ILLUMINATED (SINGLE CHANNEL FAILURE). CAPT CALLED MAINT UPON ARR AT GATE. THE CAPT MADE A COMMENT TO ME WHEN WE PICKED UP THE PLANE AT APPROX XA30 LCL THAT IT WAS AN ORIGINATING FLT (UNUSUAL); AND HAD HAD MAINT ON STABILIZER. I DON'T KNOW WHAT TYPE OF WORK AND IF THE CIRCUIT BREAKER HAD BEEN PULLED BY MAINT. WE BOTH ARRIVED AT XA25 FOR XA50 DEP (UNSCHEDULED ACFT SWAP) AND COULD HAVE MISSED THE CIRCUIT BREAKER IF IT WERE ALREADY TRIPPED. WHATEVER THE REASON THE CIRCUIT BREAKER TRIPPED; THE AUTOPLT WAS UNABLE TO LEVEL OFF AND MAINTAIN ALT WITHOUT THE TRIM OPERATING. I DON'T KNOW IF MAINT AND/OR SPD TRIM 'FAIL' WERE IN ANY WAY RELATED TO OR CAUSE OF ALTDEV/AUTOPLT FAILURE.