This monograph addresses the systematic representation of the methods of analysis developed by the authors as applied to such systems. Particular features of dynamic processes in such systems are studied. Special attention is given to an analysis of different resonant phenomena taking unusual and diverse forms. All solutions are transformed to the final analytical expressions permitting clear mechanical interpretation. These methods are applied to the analysis of mechanical systems designed for the generation and transformation of intensive impulsive processes or structures exposed to such a nonlinear dynamic loading. These are vibro-impact processes due to intermittent unilateral contacts of the structure elements, created by backlashes in joints and kinematic pairs, during opening and closing of cracks etc. New mechanical effects are described. Some engineering problems are solved using a combination of analytical technique and modern simulation tools.