This paper studies a communication model that aims at extending the scope of computational grids by allowing the execution of parallel and/or distributed applications without imposing any programming constraints or the use of a particular communication layer. Such model leads to the design of a communication framework for grids which allows the use of the appropriate middleware for the application rather than the one dictated by the available resources. Such a framework is able to handle any communication middleware — even several at the same time — on any kind of networking technologies. Our proposed dual-abstraction (parallel and distributed) model is organized into three layers: arbitration, abstraction and personalities which are highlighted in the paper. The performance obtained with PadicoTM, our available open source implementation of the proposed framework, show that such functionality can be obtained with still providing very high performance.