This text deals with a new technique for the dynamic analysis of nonlinear structures. A special feature is the technique of equivalent quadratization, which allows engineers to deal with complex nonlinear problems in a systematic manner. The applicability of this method is especially important for dealing with offshore structures which are exposed to nonlinear forces due to waves. The reader is expected to have a fundamental knowledge of calculus and some background in the area of random variables and stochastic processes. The book is intended for engineers and applied scientists who deal with nonlinear vibrations and have particular interest in the area of offshore engineering.