This book focuses on modern methods of oscillation analysis in machines, including cyclic action mechanisms (linkages, cams, steppers, etc.). It presents schematization techniques and mathematical descriptions of oscillating systems, taking into account the variability of the parameters and nonlinearities, engineering evaluations of dynamic errors, and oscillation suppression methods. The majority of the book is devoted to the development of new methods of dynamic analysis and synthesis for cyclic machines that form regular oscillatory systems with multiple duplicate modules.  There are also sections examining aspects of general engineering interest (nonlinear dissipative forces, systems with non-stationary constraints, impacts and pseudo-impacts in clearances, etc.)  The examples in the book are based on the widely used results of theoretical and experimental studies as well as engineering calculations carried out in relation to machines used in the textile, light, polygraphic and other industries. Particular attention is paid to dynamic forecasting and engineering recommendations. The book provides a link between the classic theory of oscillations and its practical application in the dynamic problems of machines.  Although it is intended for engineers and scientists who specialize in the field of machine dynamics, it will also be useful for graduate and postgraduate students.