Heterogeneity exists in almost every research computing environment. Most operating systems accommodate heterogeneity by using a coherent file system that allows clients to access source files in a transparent way. In order to allow heterogeneous computer systems to cooperate, we have applied the framework of shared virtual memory to a heterogeneous computing environment and explore in detail how to accommodate heterogeneity. We have also designed a shared virtual memory system kernel, Mermaid, upon which one can build system components, programming languages, and application software using heterogeneous computers. We are currently implementing Mermaid on a network of SUN workstations and DEC Firefly multiprocessors.