We present a system that allows task parallel OpenMP programs to execute on a network of workstations (NOW) with a variable number of nodes. Such adaptivity, generally called adaptive parallelism, is important in a multi-user NOW environment, enabling the system to expand the computation onto idle nodes or withdraw from otherwise occupied nodes. We focus on task parallel applications in this paper, but the system also lets data parallel applications run adaptively. When an adaptation is requested, we let all processes complete their current tasks, then the system executes an extra OpenMP join-fork sequence not present in the application code. Here, the system can change the number of nodes without involving the application, as processes do not have a compute-relevant private process state. We show that the costs of adaptations is low, and we explain why the costs are lower for task parallel applications than for data parallel applications.