A driving system for a vehicle comprising: a drive source (2A, 2B, 4); a driven portion (Wr), which is driven by the drive source (2A, 2B, 4) to propel a vehicle; a unidirectional power transmitting unit, which is provided on a power transmission path between the drive source (2A, 2B, 4) and the driven portion (Wr), and which is engaged when rotational power in one direction on a drive source side is inputted into a driven portion side, is disengaged when rotational power in the other direction on the power source side is inputted into the driven portion side, is disengaged when rotational power in one direction on the driven portion side is inputted into the drive source side, and is engaged when rotational power in the other direction on the driven portion side is inputted into the power source side; characterized in that: a connection/disconnection unit (60A, 60B), which is provided on the power transmission path in parallel to the unidirectional power transmitting unit so as to connect or disconnect the power transmission path by being applied or released; and a connection/disconnection unit controller, which controls a release and an application of the connection/disconnection unit (60A, 60B), wherein: the driving system further comprises a counting unit, which acquires a fact that the drive source (2A, 2B, 4) generates rotational power in the one direction whose magnitude is equal to or greater than a predetermined magnitude when the connection/disconnection unit (60A, 60B) is applied to connect the drive source side and the driven portion side together, and then which stores a generation number of times; and the connection/disconnection unit controller controls the connection/disconnection unit (60A, 60B) based on the generation number of times stored in the counting unit. a drive source (2A, 2B, 4); a driven portion (Wr), which is driven by the drive source (2A, 2B, 4) to propel a vehicle; a unidirectional power transmitting unit, which is provided on a power transmission path between the drive source (2A, 2B, 4) and the driven portion (Wr), and which is engaged when rotational power in one direction on a drive source side is inputted into a driven portion side, is disengaged when rotational power in the other direction on the power source side is inputted into the driven portion side, is disengaged when rotational power in one direction on the driven portion side is inputted into the drive source side, and is engaged when rotational power in the other direction on the driven portion side is inputted into the power source side; characterized in that: a connection/disconnection unit (60A, 60B), which is provided on the power transmission path in parallel to the unidirectional power transmitting unit so as to connect or disconnect the power transmission path by being applied or released; and a connection/disconnection unit controller, which controls a release and an application of the connection/disconnection unit (60A, 60B), wherein: the driving system further comprises a counting unit, which acquires a fact that the drive source (2A, 2B, 4) generates rotational power in the one direction whose magnitude is equal to or greater than a predetermined magnitude when the connection/disconnection unit (60A, 60B) is applied to connect the drive source side and the driven portion side together, and then which stores a generation number of times; and the connection/disconnection unit controller controls the connection/disconnection unit (60A, 60B) based on the generation number of times stored in the counting unit. a connection/disconnection unit (60A, 60B), which is provided on the power transmission path in parallel to the unidirectional power transmitting unit so as to connect or disconnect the power transmission path by being applied or released; and a connection/disconnection unit controller, which controls a release and an application of the connection/disconnection unit (60A, 60B), wherein: the driving system further comprises a counting unit, which acquires a fact that the drive source (2A, 2B, 4) generates rotational power in the one direction whose magnitude is equal to or greater than a predetermined magnitude when the connection/disconnection unit (60A, 60B) is applied to connect the drive source side and the driven portion side together, and then which stores a generation number of times; and the connection/disconnection unit controller controls the connection/disconnection unit (60A, 60B) based on the generation number of times stored in the counting unit. the driving system further comprises a counting unit, which acquires a fact that the drive source (2A, 2B, 4) generates rotational power in the one direction whose magnitude is equal to or greater than a predetermined magnitude when the connection/disconnection unit (60A, 60B) is applied to connect the drive source side and the driven portion side together, and then which stores a generation number of times; and the connection/disconnection unit controller controls the connection/disconnection unit (60A, 60B) based on the generation number of times stored in the counting unit.