We describe a parallel implementation of a genetic linkage analysis program that achieves good speedups, even for analyses on a single pedigree and with a single starting recombination fraction vector. Our parallel implementation has been run on three different platforms: an Ethernet network of workstations, a higher-bandwidth. Asynchronous Transfer Mode (ATM) network of workstations, and a shared-memory multiprocessor. The same program, written in a shared memory programming style, is used on all platforms. On the workstation networks, the hardware does not provide shared memory, so the program executes on a distributed shared memory system that implements shared memory in software. These three platforms represent different points on the price/performance scale. Ethernet networks are cheap and omnipresent. ATM networks are an emerging technology that others higher bandwidth, and shared-memory multiprocessors offer the best performance because communication is implemented entirely by hardware. On 8 processors and for the longer runs, we achieve speedups between 3.5 and 5 on the Ethernet network and between 4.8 and 6 on the ATM network. On the shared-memory multiprocessor, we achieve speedups in the 5.5 to 6.5 range for all runs.