The purpose of this part of the paper is to provide a review of recent results (1991–2003) in the applications of statistical and equivalent linearization in the analysis of structure and mechanical nonlinear stochastic dynamic systems. Both the applications in “traditional fields” of engineering and a few examples from new fields are reported. Traditional fields include vibration of construction elements, such as beams, frames, shells, and plates, and also vibration of complex structures under earthquake or wind or wave stochastic excitations, or a combination of earthquake and wind or wind and wave excitations. Typical constructions are multistory structures, offshore platforms, and vehicle models. In the paper several examples from new fields, such as vibration of wood structures, block rocking, rainfall-runoff modeling, a squeeze film model, and an astronomy model are reviewed. A discussion of typical advantages and faults of linearization techniques and some general conclusions close the paper. There are 121 references cited in this review article.