In this paper, we are interested in the computational power of a mobile agent system and, more particularly, in the comparison with a message passing system. First we give formal definitions. Then we explain how a mobile agent algorithm can be simulated by a message passing algorithm.We also prove that any message passing algorithm can be implemented by a mobile agent algorithm. As a consequence of this result, known characterisations of solvable tasks by message passing algorithms can be translated into characterisations of solvable tasks by mobile agent algorithms. We illustrate this result with the election problem.