UPON LEVELING AT 41000 FT ACFT WAS TOO HVY TO OBTAIN CRUISE SPD. A LOWER ALT WAS REQUESTED AND RECEIVED. DURING THE DSCNT; A HIGH SINK RATE ENSUED; CAUSING AN ALT OVERSHOOT.

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WE WERE CRUISING AT FL370; CLRED 'DIRECT RMG' (ROME; GA; VOR) AND HAD JUST PASSED ABEAM PUB (PUEBLO; CO) VOR. THE 'LIGHT CHOP' RIDE WAS BEGINNING TO GET WORSE AND WE WERE HANDED OFF TO ZKC. A FLT ON FREQ RPTED A GOOD RIDE AT FL410 AND WE REQUESTED FL410; WHICH WAS CLOSE TO OUR ALT LIMIT AT CURRENT WT. ZKC CLRED US TO FL410 AND I INITIATED A CLB IN 'VNAV.' CLBING THROUGH FL390 THE TURB WAS CAUSING THE AUTOPLT TO 'HUNT' THE SPD; DECREASING THE CLB RATE. I CHANGED THE AUTOPLT MODE TO 'VERT SPD/SPD' MODE. I DECREASED THE VERT SPD COMMAND FROM 1000 FPM TO 200 FPM APCHING FL410. THE SPD HAD DECREASED TO LESS THAN 220 KIAS. AT FL410 THE AIRPLANE DID NOT ACCELERATE EVEN THOUGH CLB/MAX CTL THRUST WAS SELECTED. SHORTLY THEREAFTER THE SPD BEGAN TO DECAY. I ADVANCED THE THRUST LEVERS; BUT THE EEC'S HELD THE THRUST TO 'CLB.' I TOLD THE FO THAT WE COULD NOT REMAIN AT FL410 AND HE REQUESTED A LOWER ALT FROM ATC. THE SPD CONTINUED TO DECAY BELOW 200 KIAS AND THE 'FAST/SLOW' POINTER REVERTED TO 'ALPHA' MODE. ATC SAID '4 MINS' FOR A LOWER ALT. ABOUT THEN WE BEGAN TO GET LOW SPD BUFFET. THE FO REQUESTED AN 'IMMEDIATE' DSCNT AND RESPONDED TO THE ATC REQUEST FOR REASON FOR 'IMMEDIATE' WITH 'WE CANNOT MAINTAIN FL410 WITH THIS TURB' AND ATC CLRED US TO FL370 'IN 2 MINS OR LESS.' I DISCONNECTED THE AUTOPLT AND BEGAN THE DSCNT. THE DSCNT EXCEEDED 6000 FPM AS WE ACCELERATED. I ENGAGED FLT DIRECTOR IN 'FLT CHANGE' MODE GOING THROUGH FL380; I UNDERESTIMATED THE ALT REQUIRED TO LEVEL OFF AT THAT HIGH RATE OF DSCNT AND THE DSCNT WAS STOPPED AT 36500 FT. I IMMEDIATELY RECOVERED BACK TO FL370. ATC MADE NO COMMENT ABOUT ALT. I BELIEVE THE SPD DECAY WAS DUE TO A 'MOUNTAIN WAVE' TYPE FLOW FROM EITHER THE ROCKIES OR LCL CONVECTIVE WX.