An engine-driven working machine comprising: an engine; an actuating part driven by the engine; a centrifugal clutch disposed between the engine and the actuating part; and a controller configured to detect a rotation speed of the engine to control the rotation speed, wherein when the rotation speed of the engine is higher than a predetermined clutch-in rotation speed, the centrifugal clutch connects the engine with the actuating part so as to transmit rotations of the engine to the actuating part, and wherein in a fast idling state in which the engine is operated while a throttle valve of a carburetor of the engine is maintained in a half-opened position, the controller is operated from starting of the engine in a rotation speed limitation mode in which the engine is prevented from rotating at a rotation speed that is higher than the clutch-in rotation speed, wherein in the fast idling state an increase and a decrease of the rotation speed of the engine are repeated, based on which a cycle period of rotation speed variations is defined, wherein after the throttle valve is moved to a fully-closed position by an operator's operation to allow the engine to finish the fast idling state and while the engine is in a transition state to an idling state and the rotation speed limitation mode is operated, an increase and a decrease of the rotation speed of the engine tends to be repeated, wherein thereby a cycle period of the rotation speed variations, which is longer than the cycle period of the rotation speed variations in the fast idling state, starts to be caused, characterised in that the rotation speed limitation mode is canceled by a second detection of the matter that the cycle period of the rotation speed variations of the engine is longer than the cycle period of the rotation speed variations in the fast idling state. an engine; an actuating part driven by the engine; a centrifugal clutch disposed between the engine and the actuating part; and a controller configured to detect a rotation speed of the engine to control the rotation speed, wherein when the rotation speed of the engine is higher than a predetermined clutch-in rotation speed, the centrifugal clutch connects the engine with the actuating part so as to transmit rotations of the engine to the actuating part, and wherein in a fast idling state in which the engine is operated while a throttle valve of a carburetor of the engine is maintained in a half-opened position, the controller is operated from starting of the engine in a rotation speed limitation mode in which the engine is prevented from rotating at a rotation speed that is higher than the clutch-in rotation speed, wherein in the fast idling state an increase and a decrease of the rotation speed of the engine are repeated, based on which a cycle period of rotation speed variations is defined, wherein after the throttle valve is moved to a fully-closed position by an operator's operation to allow the engine to finish the fast idling state and while the engine is in a transition state to an idling state and the rotation speed limitation mode is operated, an increase and a decrease of the rotation speed of the engine tends to be repeated, wherein thereby a cycle period of the rotation speed variations, which is longer than the cycle period of the rotation speed variations in the fast idling state, starts to be caused, characterised in that the rotation speed limitation mode is canceled by a second detection of the matter that the cycle period of the rotation speed variations of the engine is longer than the cycle period of the rotation speed variations in the fast idling state.