An EM-type gradient algorithm for analysis of maximum likelihood estimation of the two-level structural equation model with both mean and covariance structures is proposed. The model considered in this paper is a generalization of that studied by Lee and Poon (1998). Approximate standard error of the maximum likelihood estimation and the chi-squared statistic for testing the model fit are given. Simulation studies show that the proposed EM gradient algorithm converges very fast and need not be accelerated by existing techniques in the literature. Key Words: EM gradient algorithm, maximum likelihood estimation, mean and covariance structures, multilevel structural equation modeling, multivariate normal distribution # This work was supported by National Institute on Drug Abuse grants DA01070 and DA00017 + The correspondence author, E-mail: firstname.lastname@example.org 1 1. Introduction Multilevel structural equation modeling (multilevel modeling or MLM for short) has been found to be a useful tec..