Grids are more heterogeneous and dynamic than traditional parallel or distributed systems, both in terms of processors and of interconnects. A grid communication system must handle many issues: first, it must run on networks that are not yet determined when the application is launched, including user-space interconnects; second, it must transparently run on different networks at the same time; third, it should yield performance close to that of specialized communication systems. In this paper, we present NETIBIS, a new Java communication system that provides a uniform interface for any underlying inter-cluster or intracluster network. NETIBIS solves the heterogeneity issues posed by grid computing by dynamically constructing network protocol stacks out of drivers, self-contained building blocks for flexible configuration, with limited functionality per driver. We describe the design and implementation of the major NETIBIS drivers for serialization, multicast, reliability, and various underlying networks. We also describe various optimizations for performance, like layer collapsing for the GMdriver. We evaluate the performance of NETIBIS on several platforms, including a European grid.