When a mechanical system has two or more coupled vibrating components, the vibration of one of the components may destabilize the motion of the others. This destabilization effect, autoparametric resonance, is a concept that has important engineering applications. This book is the first completely devoted to the subject of autoparametric resonance in an engineering context. Using the tools of nonlinear analysis, the authors show how to carry out the first crucial step of determining the regions of parameter space where the semi-trivial solution is unstable. They describe what happens in these regions and then discuss non-trivial solutions and their stability. This text will appeal to graduate students and researchers in engineering and applied mathematics.