Membranes comprising an aromatic ether ketone polymer (e.g. polyetherketone) in sheet or hollow fibre form are made by preparing at least a 12 wt % solution of the polymer in a solvent which is chemically inert to the polymer (e.g. concentrated sulphuric acid); forming a film of the solution in sheet or hollow form; and contacting the film with a non-solvent (e.g. more dilute sulphuric acid or acetic acid) thereby to precipitate the film.