In linear mixed models, the assumption of normally distributed random effects is often inappropriate and unnecessarily restrictive. The proposed approximate Dirichlet process mixture assumes a hierarchical Gaussian mixture that is based on the truncated version of the stick breaking presentation of the Dirichlet process. In addition to the weakening of distributional assumptions, the specification allows to identify clusters of observations with a similar random effects structure. An Expectation-Maximization algorithm is given that solves the estimation problem and that, in certain respects, may exhibit advantages over Markov chain Monte Carlo approaches when modelling with Dirichlet processes. The method is evaluated in a simulation study and applied to the dynamics of unemployment in Germany as well as lung function growth data.