Abstract: A wavelet-based local stationary approach for the dynamic reliability determination of linear MDOF systems is presented. First, based on the generalized harmonic wavelet and the local stationary wavelet model of the stochastic process, an evolutionary power spectrum (EPS) density relationship between a full non-stationary excitation and response is developed. Based on the response EPS, the moments of the response EPS are calculated for the reliability determination. Finally, based on the Gaussian assumption for the linear response and Markovian assumption for the crossing event, the probability of the drift displacement remaining below a certain limit is calculated. Monte Carlo simulations demonstrate the reliability and computational efficiency of the proposed approach.