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The problem of fuel-optimal attitude maneuvering with nonfixed time is considered. The attitude of the space vehicle is controlled by means of a pair of reactive engines which produce a control torque with fixed direction in the body-fixed coordinate system. An optimal solution is obtained in the class of trajectories belonging to “swinging mode” cycling regimes. The solution is found in analytical form and optimal synthesis is obtained. The Krotov-Bellman sufficient conditions are used and the Krotov-Bellman function is found explicitly.