In the theory of random vibrations, some basic principles of the probability theory are applied. Random vibration can be represented in the frequency domain in terms of a Fourier transform or Power Spectral Density Function. In this paper we will study the nonlinear vibration of an oscillator by determining the spectral density of response. We will present the corresponding numerical results and the spectral density diagrams of the response according to the frequency. The method will be briefly discussed in the following section.