Multi-Agent Systems (MAS) promise a new advance in distributed computing. In MAS autonomous software agents flexibly cooperate, coordinate, and compete to provide the desired function(s) of such a system. If some components of a MAS fail or do not provide the desired functionality, the system is expected to autonomously deal with these situations. It is desirable to reduce occurrences of such situations by selecting trustworthy cooperation partners before cooperating with them. This becomes even more desirable and important in an open MAS where arbitrary heterogeneous software agents, deployed by different parties, participate in the MAS, as it becomes more likely that these agents fail or try to exploit the MAS for their own purposes without reciprocation. In order to monitor agent behavior and enable selection of trustworthy cooperation partners, trust or reputation management services can be applied. As there is no central control in an open MAS and it is completely distributed these services themselves have to be distributed. This paper proposes a fully distributed reputation management service for open MAS based on peer-to-peer technology (especially distributed hash tables). A Java-based implementation of that service, which is intended as a plug-in for multi-agent platforms, is also described.