Distributed networks are widely used in industrial and consumer applications. As the communication capabilities of such networks are usually limited, it is important to develop algorithms which are capable of handling the vast amount of data processing locally and only communicate some aggregated value. Additionally, these algorithms have to be robust against outliers in the data, as well as faulty or malicious nodes. Thus, we propose a robust distributed expectation maximization (EM) algorithm based on Real Elliptically Symmetric (RES) distributions, which is highly adaptive to outliers and moreover is combined with a robust data aggregation step which provides robustness against malicious nodes. In the simulations, the proposed algorithm shows its effectiveness over non-robust methods.