A power transmission system (16,202), the power transmission system being configured to transmit power between an input rotating member and an output rotating member, the power transmission system comprising: a first transmission unit provided in a first power transmission path between the input rotating member and the output rotating member; a second transmission unit provided in parallel with the first transmission unit in a second power transmission path between the input rotating member and the output rotating member; a first engagement device configured to connect or interrupt the first power transmission path that transmits power of the input rotating member to the output rotating member via the first transmission unit; a second engagement device configured to connect or interrupt the second power transmission path that transmits power of the input rotating member to the output rotating member via the second transmission unit; a third engagement device (D1, C3) configured to connect or interrupt at least one of the first power transmission path and the second power transmission path; a fail-safe valve (86,206) configured to interrupt any one of a first oil passage that supplies hydraulic pressure to the first engagement device and a second oil passage that supplies hydraulic pressure to the second engagement device such that simultaneous engagement of the first engagement device and the second engagement device is avoided; and characterized in that the power transmission system (16,202) comprises an electronic control unit configured, during traveling in a state where the third engagement device (D1,C3) is released, to output hydraulic pressure commands for simultaneous engagement of the first engagement device and the second engagement device, the electronic control unit being configured to determine whether both the first engagement device and the second engagement device are engaged at a time when the hydraulic pressure commands are being output, the electronic control unit being configured, when it is determined that both the first engagement device and the second engagement device are engaged, to prohibit traveling using said at least one of the first power transmission path and the second power transmission path which is connected or interrupted by the third engagement device (D1,C3). a first transmission unit provided in a first power transmission path between the input rotating member and the output rotating member; a second transmission unit provided in parallel with the first transmission unit in a second power transmission path between the input rotating member and the output rotating member; a first engagement device configured to connect or interrupt the first power transmission path that transmits power of the input rotating member to the output rotating member via the first transmission unit; a second engagement device configured to connect or interrupt the second power transmission path that transmits power of the input rotating member to the output rotating member via the second transmission unit; a third engagement device (D1, C3) configured to connect or interrupt at least one of the first power transmission path and the second power transmission path; a fail-safe valve (86,206) configured to interrupt any one of a first oil passage that supplies hydraulic pressure to the first engagement device and a second oil passage that supplies hydraulic pressure to the second engagement device such that simultaneous engagement of the first engagement device and the second engagement device is avoided; and characterized in that the power transmission system (16,202) comprises an electronic control unit configured, during traveling in a state where the third engagement device (D1,C3) is released, to output hydraulic pressure commands for simultaneous engagement of the first engagement device and the second engagement device, the electronic control unit being configured to determine whether both the first engagement device and the second engagement device are engaged at a time when the hydraulic pressure commands are being output, the electronic control unit being configured, when it is determined that both the first engagement device and the second engagement device are engaged, to prohibit traveling using said at least one of the first power transmission path and the second power transmission path which is connected or interrupted by the third engagement device (D1,C3).