The concept of friction in general, and the problem of stick-slip motion in particular, at microscopic length scales, are central to many areas, from friction and lubrication of materials to earthquake models and avalanches. The interest in this problem comes from the large range of physical applications that are related to it: computer disk, miniature motors, and many aerospace components. This book, therefore, provides a study of friction and stick-slip phenomena in some nonlinear models that contain nonlinear spring and deformable nonsinusoidal substrate potential, such as Remoissenet-Peyrard potential. We also provide a quite thorough description of the feature of the mechanism of frictional phenomena. We show that the critical velocities which provide the transition between stick-slip, intermittent and sliding motions depend on the shape of the contact surfaces, as well as the nonlinear parameter of the spring. This shape also affects the static friction. This analysis should help in dealing with complex situations and stimulate further experimental studies of friction and stick-slip phenomena in the deformable systems.