Determining fixed points of nonexpansive mappings is a frequent problem in mathematics and physical sciences. An algorithm for finding common fixed points of nonexpansive mappings in Hilbert space, essentially due to nalpern, is analyzed. The main theorem extends Wittmann's recent work and partially generalizes a result by Lions. Algorithms of this kind have been applied to the convex feasibility problem. (C) 1996 Academic Press. Inc.