The engageable structure of the operation rod in the pump includes a valve member having an outer sleeve as an outer valve, an inner sleeve as an inner valve installing in the outer sleeve rotatably and a pushing operation body with a sliding part installed in the inner sleeve and with a driven operation rod; a drive source; and a driving operation rod moves horizontally due to guiding by a supporting member arid force of the drive source, and a catching part of the valve member engages with a connection-supporting device which is attached to the driving operation rod when the driven operation rod of the valve member and driving operation rod of the drive source are connected. The connection-supporting device is supported pivotably at a cantilevered state to the driving operation rod at a biasing state by a spring member in the specified direction, having a vertical plate installed consecutively in a tip end portion of a pivoted plate for attachment and a locking part installed consecutively in a front surface of the vertical plate at a projecting state. Therefore, the valve member can be removed easily from the driving operation rod.