Multivariable queries can be processed in the data base management system INGRES. The general procedure is to decompose the query into a sequence of one-variable queries using two processes. One process is reduction which requires breaking off components of the query which are joined to it by a single variable. The other process, tuple-substitution, involves substituting for one of the variables a tuple at a time. The query processing algorithm has been developed for QUEL, the data language for INGRES. Algorithms for reduction and for choosing the variable to be substituted are given. The decision about which variable to substitute depends on estimation of costs, and some procedures for making cost estimates are outlined. (Author/CH)