A B737-300 FLC HAS A FAILURE OF AUTOPLT 'A' WITH 'B' MEL'ED AND A DEAD SPOT NOTICED WITHIN THE AILERON CTL SYS AFTER LEAVING LAX; CA.

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DEPARTED LAX AT XA00Z. ACFT HAD A DEFERRED 'B' AUTOPLT FOR FAILED MAINT CHKS THE NIGHT BEFORE. DEP OFF RWY 24L WAS NORMAL. CAPT WAS PF. 'A' AUTOPLT ENGAGED AT APPROX 12000 FT MSL. ZLA CLRED FLT DIRECT TO RZS. DURING TURN; CREW OBSERVED THAT 'A' AUTOPLT PITCH CTL WAS WELL BELOW PITCH STEERING BAR. VNAV ENGAGED. AS ACFT ROLLED OUT; THE STABILIZER OUT OF TRIM LIGHT ILLUMINATED FOR APPROX 10 SECONDS. THE IRREGULAR PROC WAS ACCOMPLISHED AND 'A' AUTOPLT DISCONNECTED. CAPT HAND FLEW ACFT TO CRUISE OF FL310. AT FL310; 'A' AUTOPLT WAS RE-ENGAGED (STABILIZER OUT OF TRIM LIGHT OUT); BUT ACFT IMMEDIATELY DEVIATED FROM ALT AND STABILIZER OUT OF TRIM LIGHT ILLUMINATED. 'A' AUTOPLT WAS DISCONNECTED. PHONE PATCH WAS INITIATED TO MAINT; ASKED CREW TO ENGAGE 'B' AUTOPLT. 'B' AUTOPLT ENGAGED NORMALLY WITH NO OSCILLATIONS. MAINT ADVISED THAT CREW COULD USE 'B' AUTOPLT IF NECESSARY. APPROX 5 MINS LATER; ACFT BEGAN TO DEVIATE FROM CRUISE ALT WITH STABILIZER OUT OF TRIM LIGHT ILLUMINATED. 'B' AUTOPLT WAS DISCONNECTED. CREW FELT THAT EXCEPT FOR AUTOPLT PROBS; ACFT WAS FLYING NORMALLY. DSCNT WAS INITIATED INTO SFO. AT APPROX FL200; CAPT NOTICED THAT ACFT BECAME SLIGHTLY UNSTABLE ABOUT THE ROLL AXIS. WHEN CAPT CORRECTED; A VERY NOTICEABLE DEAD SPOT WITH THE AILERONS WAS APPARENT. CAPT GAVE ACFT TO FO AND HE CONFIRMED SAME INDICATIONS. CAPT RESUMED CTL. CREW AGREED THAT AN EMER SIT EXISTED (MULTIPLE PROBS). EMER DECLARED WITH BAY APCH. DISPATCH NOTIFIED OF EMER VIA ACARS. PURSER WAS CALLED AND ADVISED OF A CABIN ADVISORY. DUE TO NATURE OF PROB (FLT CTLS); PAX WERE ONLY TOLD THAT WE WERE HAVING PROBS WITH OUR AUTOFLT SYS AND THAT WE WERE ASKING THE FLT ATTENDANTS TO PREPARE THE CABIN EARLY FOR LNDG. BAY REQUESTED THAT WE USE RWY 28L IN CASE WE HAD TO STOP ON RWY AND NOT IMMEDIATELY CLR. WX AT SFO WAS 9 OVCST AND 6 SM VISIBILITY. THE ILS APCH WAS NORMAL EXCEPT THAT APPROX 1/2 L WHEEL THROW WAS REPEATEDLY REQUIRED TO CTL ROLL AXIS OF ACFT. FUEL BAL NORMAL. LNDG WAS UNEVENTFUL. MAINT DEBRIEFED AT GATE YY. FLT ATTENDANTS DEBRIEFED IN FIRST CABIN PRIOR TO CREW DEP. I APOLOGIZED TO THEM FOR NOT TELLING THEM THE ENTIRE NATURE OF OUR PROB DUE TO THE SHORT DURATION TO LNDG AND MY SINCERE DESIRE NOT TO CAUSE EXCESSIVE CONCERN WITH OUR PROB. MY FO AND THE FLT ATTENDANTS DID A GREAT JOB AS DID ATC IN THIS MATTER. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: WHEN TALKING WITH THE MAINT DEPT THE NEXT DAY HE WAS TOLD THAT THE ACFT HAD GONE THROUGH EXTENSIVE MAINT PROCS; WITH THE SUPVR ALMOST APOLOGIZING FOR SOME AREAS OF MAINT THAT COULD HAVE BEEN MORE CLOSELY VIEWED. THE ACFT WAS CHKED OVER AND THEN TEST FLOWN WITH NOTHING FOUND IN THE WAY OF AN EQUIP PROB ASIDE FROM THE AUTOPLTS. HE STATED THAT THE B737 APPEARS TO BE 'TOLERANCE SENSITIVE' BUT HAD NEVER HAD THIS TYPE OF EXPERIENCE BEFORE. THIS ACFT HAS HAD A HISTORY OF AUTOPLT PROBS AND STABILIZER OUT OF TRIM INDICATIONS. ALL HE COULD THINK OF WAS TO NOT STRESS THE SYS AS HE DID NOT KNOW IF HE HAD A JACK SCREW PROB OR NOT. A RARE OCCURRENCE AS HE SEES THESE LIGHTS AND SITS ONLY WHEN IN THE SIMULATOR.