A B737-500 CAPT RPTS IN CLB AND CRUISE AUTOPLT PITCH CHANNELS A AND B SYS SLOW AND SLUGGISH TO CORRECT IN PITCH MODE. ON GND; FOUND STABILIZER MANUAL TRIM LOCKED.

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THE FO WAS FLYING OUR SCHEDULED LEG FROM ZZZ TO ZZZ1. DURING OUR SEVERAL STEPS OF CLBOUT OF ZZZ UP TO OUR CRUISE ALT OF FL360; WE NOTICED SEVERAL TIMES THE AUTOPLT WAS NOT AS PRECISE IN LEVELING OFF THE ACFT AS WE ARE ACCUSTOMED TO. THESE MINOR UNDER-/OVERSHOOTS WERE MAYBE 50 FT OFF. THIS WAS NOT NORMAL TO ME. WITH OVER 4000 HRS IN THE B737 IT APPEARED TO ME THAT THE AUTOPLT TRIM MOTOR WAS MAYBE NOT WORKING AS MUCH AS I NORMALLY SEE. AFTER OUR INITIAL LEVELOFF IN CRUISE; THE AUTOPLT AND ALT HOLD WORKED NORMALLY FOR THE FO AND HELD OUR ASSIGNED FL360 WELL USING THE 'B' AUTOPLT. AT APPROX XA00Z; WHILE FLYING; WE NOTICED THE ALT HOLD WAS STARTING TO NOT HOLD THE ACFT ALT AS PRECISELY. THE ACFT WAS NOW HOLDING FL360 +/-100 FT WITH A COUPLE MOMENTARY 'STABILIZER OUT OF TRIM' LIGHT ON. AUTOPLT 'A' WAS ALSO TRIED AND NO HELP. THE FO AND I AGREED THAT A MAINT WRITE-UP SHOULD BE MADE ON THIS. I COMMUNICATED TO MAINT CTLR VIA ACARS USING TEXT MESSAGES TO DESCRIBE OUR OBSERVATIONS. IT SHOULD BE NOTED THAT THE ACFT HAD PREVIOUS HISTORY ON THIS PROB NOTED IN OUR PAPERWORK SO WE MADE NUMEROUS AND DETAILED DESCRIPTIONS TO MAINT CTLR AS TO THE BEHAVIOR OF THE AUTOPLT AND TRIM SYS TO HELP IN THEIR TROUBLESHOOTING NOTES. IN SUMMARY; IT APPEARED TO ME THAT THE AUTOPLT TRIM MOTOR WAS DELAYED IN GETTING INPUTS TO THE STABILIZER TRIM AND THEN MOVED LESS THAN WHAT APPEARED TO BE NEEDED. AFTER RPTING TO MAINT CTLR ALL OUR DETAILS; THE AUTOPLT THEN SETTLED DOWN AND OPERATED NORMALLY AGAIN. AS WE APCHED TOP OF DSCNT WITH THE ALT HOLD STILL ON; THE ACFT STARTED A GENTLE CLB UP AWAY FROM OUR ASSIGNED ALT. THE FO DISCONNECTED THE AUTOPLT AT ABOUT 100 FT HIGH; TRIMMED THE PITCH DOWN NORMALLY WITH THE YOKE TRIM SWITCH AND STARTED OUR DSCNT INTO ZZZ1. THE FO FLEW A NORMAL HAND-FLOWN DSCNT TO LNDG AT ZZZ1. AT THE GATE IN ZZZ1; TALKING WITH MAINT ABOUT OUR WRITE-UP; WE NOTICED THAT THE TRIM WHEEL WAS NOW 'LOCKED' AND WE WERE UNABLE TO MOVE THE TRIM WHEELS BY HAND. POSTFLT; AS WE DISCUSSED THE VARIOUS SYMPTOMS; IT NOW SEEMS THAT THE STABILIZER TRIM BECAME SO BADLY JAMMED OR DAMAGED DURING OUR FLT; THAT THE AUTOPLT TRIM MOTOR (LOW VOLT; LOW PWR) WAS UNABLE TO MOVE THE STABILIZER TRIM AND MAY HAVE BURNED OUT. IF WE HAD NEEDED TO MANUALLY MOVE THE TRIM; IT TOO WAS LOCKED AND BEYOND OUR ABILITY TO MAKE MANUAL INPUTS. UNKNOWN TO US AT THE TIME INFLT; THE ONLY TRIM WE HAD AVAILABLE TO US WAS THE NORMAL TRIM ON THE YOKE (HIGH VOLT; HIGH PWR) AND THIS MOTOR WAS APPARENTLY WORKING VERY HARD TO GET THE JAMMED OR DAMAGED STABILIZER TRIM SYS TO MOVE AS WE NEEDED. DEPENDENT ON THE ACTUAL FINDINGS OF MAINT; IT IS POSSIBLE THAT WITH TIME; THE MAIN TRIM MOTOR COULD HAVE FAILED. ALSO; WE MAY HAVE HAD SERIOUS DAMAGE TO THE STABILIZER TRIM SYS INCLUDING THE JACK SCREW DURING OUR FLT TO ZZZ1 WHEN USING THE MAIN TRIM MOTOR. I WOULD APPRECIATE ANY FEEDBACK AS TO THE FINDINGS BY MAINT OF THE STABILIZER TRIM SYS OF THIS ACFT. THANK YOU. ADDITIONAL THOUGHTS: 1) WHAT APPEARED TO BE A MINOR PROB WITH THE AUTOPLT SYS WAS ACTUALLY A SERIOUS STABILIZER TRIM SYS PROB(S). 2) SINCE THE ACFT HAD A PREVIOUS HISTORY OF THIS 'AUTOPLT PROB;' THE ACFT FLEW MULTIPLE LEGS WITH THIS PENDING STABILIZER PROB. 3) ON MY DRIVE HOME; I REMEMBERED 2 ACFT LOST DUE TO IMPROPER TRIM SETTINGS AND/OR STABILIZER TRIM FAILURES. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED HE HAD REQUESTED FEEDBACK FROM MAINT ON THE ACTION TAKEN ON THE STABILIZER TRIM AND ANY COMPONENTS THAT HAD FAILED. RPTR HAS RECEIVED NO RESPONSE FROM MAINT ON STABILIZER TRIM FIX.