Abstract: The invention provides a process for improving the resistance to solvents in finishing and stabilizing fiber materials with textile binders, wherein the textile binder used is an aqueous copolymer dispersion or a redispersible copolymer powder of copolymers with a T.sub.g of -60.degree. C. to +60.degree. C., containing (a) one or more monomer units from the group consisting of vinyl esters of unbranched or branched carboxyli acids with 1 to 12 carbon atoms, esters of acrylic acid and methacrylic acid with unbranched or branched alcohols with 1 to 12 carbon atoms, vinyl aromatics, vinyl halides and .alpha.-olefins, and (b) 0.3 to 10 wt %, relative to the total weight of the copolymer, of one or more N-(alkoxymethyl)-acrylamides or N-(alkoxymethyl)methacrylamides with a C.sub.1 -C.sub.6 alkyl residue, or mixtures of these N-(alkoxymethyl)-meth(acrylamides with N-Methylolacrylamide and/or N-methylolmethacrylamide in a weight ratio of N-methylol compound to N-(alkoxymethyl) compound of at most 5:1.