An overview of the Triana Problem Solving Environment is provided -with a particular focus on the GAP application-level interface, for integration with Grid Computing and Peer-to-Peer infrastructure. GAP is a Javabased subset of the Grid Application Toolkit interface (being implemented in the GridLab project), and an outline of its current functionality, usage and mappings to three supported underlying middleware derivatives: JXTA, Web Services, and P2PS (a simplified Peer-to-Peer platform) are provided. The motivation behind the development of P2PS is given -emphasising its minimal, but effective Peer-to-Peer mechanisms that allow scalable, decentralized discovery and communication amongst cooperating P2PS peers within highly unstable environments. A summary of three application use cases illustrating the range of scenarios that such a system addresses is also provided.