Random loads that exhibit significant non-Gaussianity in terms of asymmetric distributions with high kurtosis can be modeled as Laplace Moving Average (LMA) processes. Examples of such loads are storm wave loadings on offshore structures. Since the loadings, and in turn, the response is random, the failure probability can be estimated from the extreme value distribution of the response. A common approach in characterizing the extreme value distributions of random processes is to study the associated first passage failures, based on the assumption that level crossings can be modeled as Poisson counting processes. The crux of the problem lies in approximating the joint pdf of the LMA process and its instantaneous time derivative. In structural systems comprising of a large number of components, the system reliability can be expressed in terms of the joint probability of exceedance of the component response processes. Usually, in structural systems such as offshore structures, the loads acting on the various components of a system have a common source and hence, the component responses and in turn, their extreme values are mutually dependent. This emphasizes the need to characterize the joint probability distribution function of the extreme values for estimating system reliability. For vector random processes, the level crossings are modeled as a multivariate Poisson process. Analytical approximations for the multivariate extreme value distribution for a vector of stationary Gaussian processes have been developed. In this study, these developments are extended to approximate the multivariate extreme value distributions for a vector of correlated LMA processes. This is illustrated through a numerical example involving a bivariate process. © 2013 Taylor & Francis Group, London.