The invention discloses a control apparatus for a power transmission system. At the time when a hydraulic actuator is operated to engage a dog clutch, after it is detected that a hydraulic pressure for operating the hydraulic actuator is higher than or equal to a predetermined hydraulic pressure, it is determined whether the dog clutch is not engaged. Therefore, non-engagement determination due to insufficient hydraulic pressure for operating the hydraulic actuator is prevented. Thus, at the time when the hydraulic actuator is operated to engage the dog clutch, it is possible to prevent consumption of time to engage the dog clutch due to unnecessary re-engagement operation.