In a hydraulic system equipped with a main flow passage for feeding oil to each of lubricated engine parts and a branch passage branched from the main flow passage, a control valve apparatus is provided for adjusting a flow rate of the oil flowing through a portion of the main flow passage downstream of the branched point. The control valve apparatus is configured to control the flow rate to a large flow-rate side of a variable flow-rate range, until a hydraulic pressure of the oil flowing through the main flow passage becomes greater than or equal to a predetermined pressure value after the engine has been started from its stopped state. The control valve apparatus is further configured to control the flow rate to a small flow-rate side of the variable flow-rate range, when the predetermined pressure value has been reached.