This invention relates to a method and a device for averting and damping rolling of an engine-driven marine vessel with propeller propulsion. The proposed method recognizes the fact that the speed controller of a ship responds to heel angle variations by propeller speed adjustments. A speed controller is reading such propeller moment change as speed variations to be corrected. By the recurrence of this process, the result is amplifying small rolling effects to a critical rolling. Further elements contribute to this process, such as the propeller side effects ship's hull contact with the sea, waves or winds. However, by suppressing the interaction between heel angle variations and the speed controller, the rolling of a ship can be effectively reduced and averted. The proposed method, by suppressing the cause of the critical rolling, reduces rolling, fuel consumption and maintenance of the ship's propulsion engines.