Described in the present application are methods of producing silane-crosslinked polymer membranes at moderate temperatures using acid catalysts that, in certain embodiments, result in membranes with unexpectedly high permeabilities and selectivities. In certain embodiments, grafting and crosslinking of the silanes occur by immersing a preformed membrane in a solution comprising a silane and an acid catalyst. Alternatively, in certain embodiments, grafting of silanes to a polymer occurs in the presence of acid catalyst in solution and subsequent casting and drying produces crosslinked membranes. In certain embodiments, an acid catalyst is a weak acid catalyst. Also described in the present application are asymmetric crosslinked polymer membranes with porous layers. In certain embodiments, crosslinked cellulose acetate membranes have permeability up to an order of magnitude greater than the permeability of unmodified cellulose acetate membranes. The membranes have porous layers with a high porosity due to their processing in moderate conditions.