The monograph sets out methods and means of technical vibrodiagnostics of machines and mechanisms based on application of nonlinear mathematical models of testing objects. The novelty of main approaches of nonlinear vibrodiagnostics is revealed. It is shown, that within nonlinear approach a great number of effective and sensitive diagnostic signs can be received. Utilization of nonlinear effects makes it possible to increase the reliability of vibration testing and reduce the laboriousness of diagnostic procedures. The examples of practical application of the proposed diagnostic methods are presented (detection of fatigue cracks in aviation structures and rotating shafts, nondestructive testing of technical condition of kinematic pairs with nonlinear elastic and dissipative characteristics, determination of moisture content in materials, etc.). The majority of proposed methods and means of diagnostics are patented and adopted in leading engineering plants of Latvia and Russia. The book is intended for researchers and engineers concerned with development and practical use of hardware for technical diagnostics of machines and mechanisms. It also can be used by students of doctoral and master studies as manual in disciplines “Experimental mechanics and technical diagnostics”, “Dynamics and strength of machines”, etc.