We investigate the issues involved in developing a scalable World Wide Web (WWW) server on a cluster of workstations and parallel machines. The objective is to strengthen the processing capabilities of such a server by utilizing the power of multicomputers to match huge demands in simultaneous access requests from the Internet. We have implemented a system called SWEB on a distributed memory machine, the Meiko CS-2, and networked workstations. The scheduling component of the system actively monitors the usages of CPU, I/O channels and the interconnection network to effectively distribute HTTP requests across processing units to exploit task and I/O parallelism. We present the experimental results on the performance of this system.