A method for controlling an engine unit (EU) for a straddled vehicle , the engine unit (EU) comprises an engine having a crankshaft and a rotating electrical machine power-transmittably coupled to the crankshaft , configured to be used in common as a starter motor for rotating the crankshaft , and as a generator for generating electric power by a rotating force of the crankshaft ; the method comprises: executing, in response to a start trigger operation of an operating member , when the engine is in a stopped state, a start cranking control (S61 to 65, S71) of energizing the rotating electrical machine to drive the crankshaft in a forward rotation direction so as to start the engine , executing, after the engine is stopped and before beginning the drive of the crankshaft in the forward rotation direction, a swing back control (S19, S22, S67, S31 to S35) of driving the crankshaft in a reverse rotation direction by the rotating electrical machine to rotate the crankshaft in reverse, wherein the swing back control is performed between a point at which the engine is put in the stopped state and a point at which the engine is started subsequently by performing the start trigger operation by the operating member , and characterized in that the method further comprises: in the start cranking control (S61 to S67, S71), continuing the energization of the rotating electrical machine until a predetermined cranking limit time, determined such that the engine begins combustion, elapses, even if the start trigger operation of the operating member is eliminated, wherein, if, in the start cranking control (S61 to S67, S71), the start trigger operation of the operating member is continued until after the predetermined cranking limit time elapses without the engine beginning the combustion, continuing the energization of the rotating electrical machine until the start trigger operation is eliminated. executing, in response to a start trigger operation of an operating member , when the engine is in a stopped state, a start cranking control (S61 to 65, S71) of energizing the rotating electrical machine to drive the crankshaft in a forward rotation direction so as to start the engine , executing, after the engine is stopped and before beginning the drive of the crankshaft in the forward rotation direction, a swing back control (S19, S22, S67, S31 to S35) of driving the crankshaft in a reverse rotation direction by the rotating electrical machine to rotate the crankshaft in reverse, wherein the swing back control is performed between a point at which the engine is put in the stopped state and a point at which the engine is started subsequently by performing the start trigger operation by the operating member , and in the start cranking control (S61 to S67, S71), continuing the energization of the rotating electrical machine until a predetermined cranking limit time, determined such that the engine begins combustion, elapses, even if the start trigger operation of the operating member is eliminated, wherein, if, in the start cranking control (S61 to S67, S71), the start trigger operation of the operating member is continued until after the predetermined cranking limit time elapses without the engine beginning the combustion, continuing the energization of the rotating electrical machine until the start trigger operation is eliminated. <EOS>