A B737-800 CREW SUBMITTED RPTS DESCRIBING HOW THEY NEARLY STALLED AS THEY ATTEMPTED TO CAPTURE THEIR CRUISING ALT.

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I AM RELATIVELY NEW TO FMC AUTOMATED FLT; AND THEREFORE; DID NOT REACT FAST ENOUGH TO AN AUTOMATION FAILURE THAT PRODUCED AN ALTDEV UPON LEVELOFF. I HAD SELECTED MAX RATE CLB ON THE FMC UPON A CTR REQUEST FOR 'GOOD RATE.' WHILE CLBING THROUGH ABOUT FL345 FOR FL350; I OBSERVED AIRSPD FALLING OFF FROM THE MAX RATE COMMAND BUG AT A RAPID RATE. NOSE WAS ALSO PITCHING UP. WE MANAGED TO REACH FL349 BUT AT A VERY LOW ENERGY STATE; WITH 'BUFFET WARNING' ANNUNCIATED ON THE EICAS DISPLAY. PRIOR TO REACHING THIS CONDITION; I WAS INVOLVED IN RESELECTING THE CLB PAGE WITH A VIEW TO REINSTATING ECONOMY CLB ON THE FMC. HOWEVER; THE ACFT NEEDED IMMEDIATE ATTN DUE TO THE RAPIDITY OF THE ENERGY LOSS. I WAS INTENT OF REDUCING PITCH RIGHT AWAY; SO I DISENGAGED THE AUTOPLT TO ESTABLISH MANUAL FLT. AUTOMATIC FOLLOW-UP PITCH TRIM HAD NOT YET HAD TIME TO CATCH UP TO THE NEW LOW ENERGY STATE; AND SO I WAS IMMEDIATELY PRESENTED WITH STRONG NOSE DOWN PITCH FORCES. THIS CAUSED THE NOSE TO DROP A LITTLE MORE THAN I HAD PLANNED OR WOULD HAVE DESIRED; AND ALT DECREASED TO ABOUT FL345 AGAIN. THIS WAS NOT NECESSARILY A BAD THING AERODYNAMICALLY SPEAKING; HOWEVER; I AM AWARE THAT CTR WAS OBLIGED TO ISSUE AN AVOIDANCE VECTOR TO ANOTHER CARRIER AT THE TIME. A FACTOR IN THIS INCIDENT WAS MY RELATIVE SLOWNESS; UPON OBSERVING THE AIRSPD DECREASE AND PITCH UP; IN SELECTING CLB PAGE IN ORDER TO INSTITUTE A FIX. I THINK I WAS MOMENTARILY TRANSFIXED BY THE PHENOMENON OF THE AIRSPD NEEDLE JUST DROPPING OFF THE COMMAND BUG; AND DROPPING FAST. 'IT JUST WASN'T SUPPOSED TO DO THAT.' BY THE TIME I HAD ASSIMILATED THIS INFO AND INTEGRATED IT; WE HAD GAINED ANOTHER 500 FT AND THE ACFT NOW NEEDED IMMEDIATE ATTN. THIS WAS A FIRST FOR ME IN THIS ACFT -- TO OBSERVE THE AUTOPLT ALL OF A SUDDEN START IGNORING AN FMC COMMAND AND GO OFF ON ITS OWN -- WITH NO OTHER FAILURE INDICATIONS. SUPPLEMENTAL INFO FROM ACN 449583: WHILE CLBING TO FL350 THE CAPT WHO WAS FLYING OBSERVED AIRSPD BEGIN TO DECREASE PASSING FL345. THE AUTOPLT WAS IGNORING THE FMS COMMANDED AIRSPD OF 260 KTS AND RAISING THE PITCH. THE FMS WAS DIRECTING A MAX RATE CLB AT THE TIME. THE CAPT DISCONNECTED THE AUTOPLT TO REGAIN AIRSPD AND THE ACFT DSNDED FROM FL349 TO APPROX FL345 WHERE AIRSPD BEGAN TO RECOVER. AT THIS TIME; I DO NOT KNOW WHY THE AUTOPLT IGNORED THE FMC AND BEGAN REDUCING AIRSPD. THE ALT LOSS WAS A RESULT OF THE LOW AIRSPD AND THE NEED TO RECOVER IT ABOVE A SAFE BUFFET MARGIN. I COULD HAVE IMPROVED THE SIT BY RECOGNIZING THE AIRSPD LOSS SOONER AND BRINGING IT TO THE CAPT'S ATTN. BETTER CRM NEEDED ON MY PART.