The most common oscillations of the mechanical systems are inherently nonlinear. These systems are important in engineering because many practical engineering components consist of vibrating systems that can be modeled using oscillator systems such as elastic beams supported by two springs or mass-on-moving belt or nonlinear pendulum and vibration of a milling machine. Therefore, investigating the nonlinear oscillations is important for many practical engineering components. The fluctuation, stability and the natural frequencies are very important items in oscillations of the mechanical systems, and investigating the influence of different parameters on these items is important in the design step. In the present book, nonlinear oscillation and stability analyses of dynamical systems are analyzed using an analytical approach. The results show that this method is very effective and work very well for the wide range of time and boundary conditions for various strongly nonlinear oscillators.