AN important challenge in the preparation of porous polymer membranes for technological applications is to control both the size distribution and the relative positions of the pores. We have found a way to generate polymer films with an essentially monodisperse pore size, in which the pores are organized spontaneously into periodic hexagonal arrays. The films, which are 10-30 mu m thick, are produced by evaporating solutions of star-shaped polystyrene or polystyrene-polyparaphenylene block copolymers in carbon disulphide under a flow of moist gas. Empty spherical cells, about 0.2-10 mu m in diameter, appear spontaneously in a hexagonal array, and the cells are open at the film surface. The use of star polymers, or of polymeric micelles, seems to be essential for obtaining this morphology. These membranes might find application in controlled release of drugs or other bioactive species, or as materials with useful optical properties, moulds or scaffolding for forming ordered microstructures, and model substrates for surface science.