New methods for mathematical simulation of vibrations in complex nonlinear mechanical systems are proposed. These methods take into account physical and geometrical nonlinearities of machine elements, limited power of excitation source, existence in the system’s structure of sufficiently nonlinear elastic and dissipative ties, etc. The monograph is devoted to analysis of nonlinear dynamic effects in mechanical systems and further practical application of these effects in vibration engineering. It is shown, that utilizing of specific nonlinear properties of subharmonic regimes (complex vibration spectrum, essential asymmetry of time response, predominance of low frequency harmonic components in vibration spectrum, etc.) ensures more effective operation of vibration machines for different technological purposes (vibrocompaction, vibroforming, vibration cleaning, etc.). The perspective of a design of new reversible vibroconveyers, based on using of nonsymmetrical subharmonic regimes, is estimated. Three interconnected nonlinear effects (contraction of the ambiguous zone, increasing of the dynamic stability, guaranteed stable start) are considered. These effects take place in the zone of main resonance. The new technological vibration machines, which apply nonlinear effects, are designed. Parametric and forced oscillations of flexible elements (belts, cables, guy ropes, filaments, strings, etc.) are studied. The new effect of vibration stabilization of oscillations in nonlinear system is discovered. The possibilities for practical application of this effect to suppress of nonlinear parametric oscillations of flexible elements are shown. The dynamics of vibration machines with parametric excitation is studied. The main advantages of parametric vibromachines are shown. The novelty of engineering designs and methods described in the monograph is confirmed by more than 50 patents of the USSR and Latvia. Some engineering designs are adopted in industry.