The present invention relates to a feed screw driving apparatus that moves a power transmission member, which engages a feed screw, in an axial direction of the feed screw by rotationally driving the feed screw using a driving source, such as an electric motor, and also to an information recording and/or reproducing apparatus that moves a pick-up apparatus with this feed screw driving apparatus and records and/or reproduces an information signal onto or from a disc-like recording mediumIn a feed screw driving apparatus that moves a power transmission member, which engages a feed screw, in an axial direction of the feed screw by rotationally driving the feed screw using a driving source, there is provided an elastic member that energizes the power transmission member in the axial direction of the feed screw.The gap between the feed nut and the feed screw is eliminated, so that the feed screw can be driven at high speed without driving errors (play) being produced and the driving of a slide member can be controlled with high precision.