The study of nonlinear problems is of crucial in the areas of Applied Mathematics, Physics and Engineering, as well as other disciplines. The differential equations are linear or nonlinear, autonomous or non-autonomous. Practically, numerous differential equations involving physical phenomena are nonlinear. Methods of solutions of linear differential equations are comparatively easy and highly developed. Whereas, very little of a general character is known about nonlinear equations. An important approach to the study of such nonlinear oscillations is the small parameter expansion of Krylov-Bogoliubov-Mitropolski (KBM). This book is concerned the critically damped nonlinear systems by use of the KBM method. The presentation of this book is easy and intelligible by the beginners. Researchers who thoroughly cover the book will be well prepared to make important contributions to analyze nonlinear systems. It will be helpful in the area of mechanics, physics, engineering etc. The book contains a wide bibliography.