A hydraulic apparatus for adjusting the timing of opening and closing of an engine valve includes a cam shaft driven to rotate in synchronization with the engine rotation. An actuator is installed on the cam shaft for changing the timing of opening and closing of an intake valve and/or exhaust valve using a control of a working oil supply. A slidable plunger is disposed in the actuator, and a rotor is disposed in the actuator to engage with the plunger by an engaging hole. A spring urges the plunger to move into the engaging hole to make an engagement therebetween when the engine is stopped, and when the engine begins to run, the working oil is supplied into the engaging hole to push out the plunger from the engaging hole to release the engagement between a housing of the actuator and the rotor. The engaging hole and the plunger have a surface parallel with a slide direction of the plunger, and a clearance therebetween is smaller than 0.17 mm when the engaging hole and plunger engage each other.