A valve opening and closing time control apparatus includes; a relative rotation angle control unit performs most delayed angle setting control of setting a relative rotation angle between a driving side rotating body and a driven side rotating body to the most delayed angle when performing an automatic stop, and most delayed angle restriction control of maintaining the relative rotation angle in the most delayed angle from a beginning of the automatic start until reaching a set timing when the automatic start-up begins, and releasing a maintenance of the most delayed angle after the setting timing.