A process for the dyeing of fiber materials with water-soluble anionic dyes, in particular those having a fiber-reactive group, is described, according to which dyeing is carried out using low-electrolyte or entirely electrolyte-free and/or low-alkali or entirely alkali-free dye solutions (dye liquors, printing pastes) and in which a fiber material is used which was modified by means of a saturated straight-chain or branched aliphatic or cycloaliphatic compound which is unsubstituted or substituted by one or more hydroxy groups and contains at least one primary, secondary or tertiary amino group or quaternary ammonium group and at least one hydrolyzable ester group, it also being possible for the aliphatic radical in this compound to be interrupted by one or more hetero groups. Modifikation of the fiber material is carried out such that the aliphatic compound mentioned which contains amino and ester groups is applied to the fiber material in aqueous solution and the impregnated material is subjected to a heat treatment. Furthermore, a few new aliphatic compounds containing amino and ester groups are described which can be used for the modification of the fiber material.