What was found
DOV/RMS DIVERSION TO JFK, IN CRUISE AT FL350 NR 1 ENGINE BEGAN TO SHUDDER/STALL WITH DROP OF N1 ONLY. PULLED THRUST LEVER BACK. IT THEN DID IT AGAIN AND CONTINUED TO DO IT. SHUT DOWN ENGINE IAW QRH. DIVERTED TO JFK. NO FUEL DUMPED. REMOVED AND REPLACED NR 1 ENGINE PER ATLAS AIR TASK CARD 01-AA-45. ACCOMPLISHED GROUND RUN UP TESTES 3, 4 AND 8 PER MM 71-00-00. OPS AND LEAK CHECK NORMAL. NO DEFECTS NOTED. CLOSED AND SECURED ALL PANELS, COWLINGS AND FAIRINGS. ENGINE S/N ON 517265. (M)