Abstract: A process for improving the biocompatibility of cellulosic film membranes is characterized by the fact that the film membranes are coated during or after their preparation with cellulose ethers and/or cellulose esters and/or cellulose carbamates whose structures conform to the formulas ##STR1## wherein Cell is the skeleton of the unmodified cellulose molecule without hydroxyl groups; x conforms to the degree of modification, which is in the range of 0.002 to 3; R is an (optionally substituted) alkyl and/or alkenyl and/or aryl and/or arylalkyl group and the carbon chain of the group R contains 1 to 36 carbon atoms and may be interrupted by hetero atoms such as O, S, N, and contains basic and/or acidic groups such as 13 NR'.sub.2, --COOR', and/or --SO.sub.3 R' or their salts, wherein R'=H or R.