The present invention relates to use of an aqueous polymer composition containing a water-soluble or water-dispersible polymer P made of polymerized ethylenically unsaturated monomers M comprising. 30 to 90 wt.-%, based on the total weight of monomers M, of at least one monomer M1 selected from C1-C12-alkyl esters of monoethylenically unsaturated carboxylic acids, C6-C10-cycloalkyl esters of monoethylenically unsaturated carboxylic acids and monovinylaromatic hydrocarbon monomers, 5 to 30 wt.-%, based on the total weight of monomers M, of at least one monomer M2 selected from monoethylenically unsaturated monomers containing at least one acid group, and 5 to 40 wt.-%, based on the total weight of monomers M, of at least one monomer M3 different from M2 which has a reactive functional group being capable of being crosslinked, wherein the total weight of monomers M1, M2 and M3 corresponds to at least 90% of the total weight of monomers M; wherein the monomers M are selected such that the theoretical glass transition temperature according to Fox (Tgt) of the polymer P is at most 80° C.; and wherein the polymer P is dissolved or dispersed in an aqueous phase such that the acid groups of the polymer P are totally or partially neutralized; as a staining composition for porous materials. The present invention also relates to an aqueous polymer composition containing said water-soluble or water-dispersible polymer P made of polymerized ethylenically unsaturated monomers M and a crosslinking agent.