B737 FLC INCORRECTLY OPERATE AUTOPLT RESULTING IN AN ALT OVERSHOOT.

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WE WERE LEVEL AT 13000 FT MSL AND ACCELERATING TO ENRTE SPD. ZLA GAVE US A CLRNC TO CLB AND MAINTAIN 16000 FT MSL. I STARTED A CLB TO 16000 FT AND CONTINUED TO ACCELERATE. THE 'A' CHANNEL AUTOPLT WAS BEING USED WITH CTL COLUMN INPUTS BEING USED TO MANEUVER THE ACFT. I WAS RETURNING MY NAV RADIOS WHEN I NOTICED THE AIRPLANE GOING THROUGH 16000 FT MSL. THE ALT ACQUIRE MODE APPEARED TO BE ENGAGED BUT THE AUTOPLT HAD NOT CAPTURED THE ASSIGNED ALT 16000 FT MSL. I DISENGAGED THE AUTOPLT; STOPPED THE CLB AND INITIATED THE DSCNT BACK TO 16000 FT MSL. WE REACHED ABOUT 16800 FT MSL BEFORE I WAS ABLE TO STOP THE CLB. CTR ASKED US ABOUT OUR ALT AND TOLD US WE HAD BEEN ASSIGNED 16000 FT MSL. HE THEN GAVE US A CLRNC TO MAINTAIN 17000 FT MSL; WHICH WE DID. I DO NOT KNOW IF THE RATE OF CLB WAS TOO HIGH FOR THE AUTOPLT TO CAPTURE THE ASSIGNED ALT OR IF I INADVERTENTLY APPLIED YOKE PRESSURE AND CAUSED IT TO MISS THE ALT. IN ANY CASE; I SHOULD HAVE PAID MORE ATTN TO THE LEVELOFF PROCESS. I COULD HAVE AVOIDED MY ALTDEV. THE AUTOPLT ACTED NORMALLY FOR THE REST OF THE FLT. SUPPLEMENTAL INFO FROM ACN 526976: PASSING 15000 FT WITH A 5000 FPM CLB RATE; AUTOPLT WENT TO 'ACT' ACQUIRE MODE; BUT FAILED TO LOWER THE NOSE.