Membranes are based on a homogeneous mixture of polyvinylidene fluoride and a second polymer which can be rendered hydrophilic by chemical reaction. The membranes contain 70 to 98 percent by weight of polyvinylidene fluoride and 2 to 30 percent by weight of a polymer formed essentially from polymethyl and/or polyethyl acrylate, and have a maximum pore size in the range from 0.005 to 10 .mu.m. They can be rendered hydrophilic by means of at least partial hydrolysis, at least partial transesterification with an alcohol which is at least trihydric and contains 3 to 12 carbon atoms, and/or at least partial aminolysis with an amino compound having 2 to 8 carbon atoms. The flat or capillary membranes which have been rendered hydrophilic can contain on their total surface 0.001 to 10 milliequivalents/g of membrane, preferably 0.01 to 5 m equivalents/g of membrane, of --COOH, --OH or --NH.sub.2 groups or corresponding mixtures of these hydrophilic functional groups. Such membranes can be used, in particular, for immobilizing biochemically active compounds.