Permselective asymmetric membranes suitable e.g. for hemodialysis, hemodiafiltration and hemofiltration of blood, and having improved sieving characteristics providing enhanced removal of middle molecular weight substances, e.g. inflammatory mediators having a molecular weight between 20 and 40 kDa. The membranes comprise polyethersulfone and polyvinylpyrrolidone and are coated with hyaluronic acid or copolymers of 2-methacryloyloxyethyl phosphoryl choline and other vinyl polymerizable monomers. Processes for the preparation of these membranes, devices comprising these membranes, and the use of these membranes in hemodialysis, hemodiafiltration and hemofiltration of blood, as well as in bioprocessing, plasma fractionation and the preparation of protein solutions.