The design of the Gamma database machine and the techniques employed in its implementation are described. Gamma is a relational database machine currently operating on an Intel iPSC/2 hypercube with 32 processors and 32 disk drives. Gamma employs three key technical ideas which enable the architecture to be scaled to hundreds of processors. First, all relations are horizontally partitioned across multiple disk drives, enabling relations to be scanned in parallel. Second, parallel algorithms based on hashing are used to implement the complex relational operators, such as join and aggregate functions. Third, dataflow scheduling techniques are used to coordinate multioperator queries. By using these techniques, it is possible to control the execution of very complex queries with minimal coordination. The design of the Gamma software is described and a thorough performance evaluation of the iPSC/s hypercube version of Gamma is presented.>