The two stage group-screening procedure is extended to multiple stages for the case when responses are observed with negligible error. Because of their potential usefulness, three and four stage procedures are treated in some detail. The generaln+ 1 stage procedure is defined, a formula is developed for the expected number of runs, and for a fixed number of factors is minimized with respect to the sizes of the group-factors at various stages. Finally the procedures at different stages are compared with respect to the minimum expected number of runs.