Composite cellulosic semipermeable membranes are disclosed which are the covalently bonded reaction product of an asymmetric cellulosic semipermeable membrane and a polysiloxane containing reactive functional groups. The two reactants chemically bond by ether, ester, amide or acrylate linkages to form a siloxane-grafted cellulosic membrane having superior selectivity and flux stability. Selectivity may be enhanced by wetting the surface with a swelling agent such as water.