Algorithms are described and analyzed for the efficient evaluation of the project and join operators of a relational algebra on a proposed non-von Neumann machine based on a hierarchy of associative storage devices. This architecture permits an O (log n ) decrease in time complexity over the best known evaluation methods on a conventional computer system, without the use of redundant storage, and using currently available and potentially competitive technology. In many cases of practical import, the proposed architecture may also permit a significant improvement (by a factor roughly proportional to the capacity of the primary associative storage device) over the performance of previously implemented or proposed database machine architectures based on associative secondary storage devices.