Strategy for processing multivariable queries in the database management system INGRES is considered. The general procedure is to decompose the query into a sequence of one-variable queries by alternating between (a) reduction: breaking off components of the query which are joined to it by a single variable, and (b) tuple substitution: substituting for one of the variables a tuple at a time. Algorithms for reduction and for choosing the variable to be substituted are given. In most cases the latter decision depends on estimation of costs; heuristic procedures for making such estimates are outlined.