Described herein is a laser machine tool for carrying out cutting or welding operations, in which a laser head (17) is carried by a moving member (5) which is displaceable with respect to a workpiece (L) along two horizontal cartesian axes (X, Y) in a relatively wide space with movements involving relatively low accelerations. The laser head (17) is displaceable on the moving member (5), along a pair of horizontal cartesian axes in a relatively restricted space with high speeds and accelerations, via a pair of slides (11, 12) to which respective balancing weights (20, 21) are operatively associated.