The doctoral thesis cover new previously unknown fundamental laws governing the behavior of the pendulum driven systems in the framework of the interdisciplinary science “nonlinear dynamics and chaos”. The bifurcation theory of nonlinear dynamical systems and the method of complete bifurcation groups developed in Institute of Mechanics of Riga Technical University are used for the global analysis of driven damped pendulum systems with one or several degrees of freedom. New nonlinear effects have been found for parametrically excited pendulum systems with the periodically vibrating point of suspension in different directions (in vertical, in horizontal, in both directions and at a certain angle to the horizontal), pendulum with external harmonic excitation, rigid body pendulum with several equilibrium positions, centrifugal pendulum vibration absorber, pendulum model with a additional sliding mass, double pendulum with harmonic oscillations of the point of suspension in the vertical direction, six body pendulum system with several equilibrium positions and harmonic excitation. The birth of the previously unknown rare attractors has been shown for different pendulum systems, and new bifurcation groups with complex protuberances have been obtained. The new types of interaction of different oscillating and rotating orbits have been found as well as rare and chaotic rotating regimes. Also the process of formation of chaotic rotation through the cascade of period-doubling bifurcations for different groups has been studied within the framework of the research. Also attention is paid to stable periodic and chaotic oscillations of different type near unstable equilibrium position of the pendulum. The doctoral thesis are intended for use in a course of ordinary differential equations, in courses on nonlinear dynamics and chaos and in nonlinear oscillation theory for students of different specialties who have basic knowledge to the extent of the 1st year of training at technical colleges and universities, as well as for those interested in contemporary issues and methods of nonlinear oscillation theory and nonlinear dynamics and chaos. This doctoral thesis obviously does not cover the topic fully and author will be grateful for remarks. This doctoral thesis can be useful for illustrating the main statements of the bifurcation theory of nonlinear dynamical systems, which is a rather new section of the general theory of nonlinear dynamical systems.