In this paper we study reciprocation-based mechanisms to encourage donation in peer-to-peer grids in which multiple services, such as processing power and data transfers, are shared explicitly. We have modeled such a system and established how peers should assess whether it is profitable to exchange services with another peer, an issue that is not present in the single service case. Unfortunately, this assessment relies on information provided by untrustworthy peers. As an alternative, we have extended, to the case of multiple services, a reciprocation-based mechanism which uses only reliable information gathered locally. We have assessed this mechanism by simulating scenarios in which services are exchanged that are combinations of two different basic services. In the explored scenarios the mechanism performs very well, and can marginalize free riders even when the cost to peers of donating a service is nearly as large as the utility gained by receiving it.