Several recent parallel computers have implemented logically shared, physically distributed memory systems which allow processors to directly access memory in other processors without interrupting the referenced processing element. Because this kind of architecture provides greater flexibility for interprocessor communications than private address space computers, different software models can be developed to take advantage of these machines. In this paper, we describe a low-level collective communications interface called SLICC (Shared address-space Library Interface for Collective Communications), that is specifically tailored for shared memory parallel computers. We also provide performance results for an implementation on the Cray T3D and compare its performance to Cray's PVM implementation. These results show that SLICC can be more than 10 times faster than PVM on the T3D.>