When the outer lid of a container closure is moved from a closed position for covering the upper surface wall of the body to an open position, the inner lid is moved from a closed position for closing a discharge port at the tip to an open position for opening the discharge port; and when the outer lid is moved from the open to the closed position, the inner lid is moved from the open to the closed position, the inner lid is prevented from becoming twisted. A second hinge connecting the inner lid to the discharge tube includes a central hinge piece connecting the inner lid and the discharge tube in a widthwise central part of the inner lid, and opposite side hinge pieces connecting the inner lid and the discharge tube on both outer sides in the width direction.