Abstract: Disclosed are heat-resisting porous membranes or hydrophilized heat-resisting porous membranes comprising a polyolefin, especially a polyethylene or a polypropylene membrane having a crosslinked polymer held thereon, the crosslinked polymer being composed principally of (a) a polymerizable monomer containing one acid anhydride group or two esterified carboxyl groups or a monomer having at least one carboxylic group and (b) divinylbenzene, or of (a), (b) and further (c) styrene or a derivative thereof, or of (b) and (c). These membranes are prepared by thermally polymerizing some of monomer components from (a) through (c) held on at least a part of the surface of the porous membranes and optionally by further hydrophilizing the crosslinked polymer. The resulting porous membranes are useful for membrane separation requiring steam sterilization and for membrane separation of water of a high temperature.