Our language model is primarily aimed at distributed memory computers, including networks of workstations or PCs. Clearly the Java version of HPspmd also holds special promise in the domain of metacomputing--targeting heterogeneous systems. At the other extreme, the same model can be straightforwardly implemented on symmetric multiprocessors--using threads within a single Java virtual machine. The most naive approach is to directly simulate the SPMD model in this environment with a fixed set of threads. Further possibilities arise if a few restrictions on variable usage are added to the language model. The main program can execute as a single thread, with multiple threads forked only when an overall construct is encountered. These issues will be investigated further.