Abstract: Composite polymer membranes are disclosed comprising a first polymeric material which defines a porous matrix, and a second polymeric material which at least partially fills, and thereby blocks, the pores of the matrix, and in which preferably each of the first and second materials are crosslinked. The membrane preferably includes a layer of an ethylenically unsaturated carboxylic acid which is graft-polymerized with the first polymeric material of the porous matrix on one of its surfaces. Crosslinking has been found to improve the transport characteristics of species through the membrane, such as the barrier performance of the membrane towards species dissolved in solution.