The problem of linear stluctural systems subjected to ealthquake excitation has been studied using different models for the eathquake excitation, from stationaq random processes to nonstationaq random process, and the subject has fairly well covered by many researchers in the past.
However, when the system is a non-linear stlucture under the action of non-stationary random excitation the research is still going on, and there are much less studies than for the linear case. In this work a method to compute the statistics of the response of a SDOF non linear system is presented. In this case it is assumed that the response can be modeled as a Markov random process, this assumption leads first to the Chapman Kolmogorov equation which in turns leads to the Fokker Planck differential equation that controls the transition probability density function of the displacement and velocity of the system. The earthquake acceleration used as excitation to the oscillator is modeled as a nonstationaq Gaussian distributed random process, using a model proposed by Der Kiureghian and Crempien (1989) and modified later by Crempien and Orosco (2000).