We examine maximum likelihood estimation procedures in multilevel models relatedbto two-level hierarchically structured data. Usually, for fixed effects and variance components estimation, multivariate normal distribution is assumed. Here we consider for random effects multivariate exponential power distribution (MEP), which represents one of the possible generalizations of multivariate normal distribution. We examine robustness of maximum likelihood estimators under normal assumption when, indeed, random effects are MEP distributed. The study is conducted through MC simulation procedures.