A novel composite membrane without continuous pores (see figure) with very high permeance for hydrogen is reported. The membrane is composed of a thin (30 nm) permselective silica layer deposited on a graded gamma-alumina multilayer substrate, consisting of size-controlled boehmite (AlOOH) sols deposited in order of decreasing size on a macroporous alumina support. A theory involving jumps of permeating molecules between adjacent solubility sites explains its behavior.