As grid sizes increase, the need for self-organization and dynamic reconfigurations is becoming more and more important, and therefore the convergence of grid computing and Peer-to-Peer (P2P) computing seems natural. Grid infrastructures are generally available as a federation of SAN-based clusters interconnected by high-bandwidth WANs. However, P2P systems are usually running on the Internet, with a non hierarchical network topology, which may raise the issue of the adequacy of the P2P communication mechanisms on grid infrastructures. This paper evaluates the communication performance of the JXTA P2P platform over high-performance SANs and WANs, for both J2SE and C bindings. We analyze these results and we evaluate solutions able to improve the performance of JXTA on such networking grid infrastructures.