A B737-800 AT FL370 APCHED A STALL CONDITION AS IT TURNED AND LEVELED FOLLOWING A CLB. ACFT DSNDED APPROX 400 FT DURING RECOVERY.

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AT FL330; ATC REQUESTED WE CLB TO FL370 AND BE LEVEL BY XA45Z. VERT SPD WAS SELECTED. AFTER CLB WAS INITIATED; ATC INSTRUCTED US TO TURN 15 DEGS L FOR OUR CLB; AND UPON REACHING FL370 CLRED DIRECT ZZZ. AT 36800 FT; I NOTICED AIRSPD DROPPING BELOW SELECTED SPD BUG; AND ADVISED THE CAPT 'WATCH YOUR AIRSPD.' AT THAT TIME WE WERE AT LEAST 5 KTS ABOVE THE YELLOW HOOK. THE CAPT SELECTED LNAV. I BELIEVE HE DID THIS BECAUSE THE ACFT WAS STARTING TO LEVEL OFF AT FL370 AND THE AIRSPD WAS ABOVE THE YELLOW HOOK. AS THE ACFT TURNED TO INTERCEPT THE COURSE; WITH AUTOPLT AND AUTOTHROTTLES ENGAGED; WE FELT WHAT MAY HAVE BEEN A BUFFET FOR ABOUT 1-2 SECONDS. I'M NOT SURE IF THE BUFFET WAS CAUSED BY THE FLT SPOILERS DEPLOYING IN THE BANK; THE LIGHT CHOP WE WERE IN; OR THE AIRSPD. AS THE WINGS STARTED TO ROLL LEVEL; WE HAD AN 'A' APPEAR IN THE SPD SELECT WINDOW; INDICATING THE AIRSPD HAD SLOWED INTO THE YELLOW HOOK. THE AUTOPLT LOWERED THE NOSE TO PROTECT THE SPD. THE CAPT IMMEDIATELY DISCONNECTED THE AUTOPLT; CONTINUED TO ROLL THE WINGS LEVEL; AND RETURNED THE ACFT TO FL370. THE ACFT HAD DSNDED APPROX 400 FT.