The present invention relates to a process for the preparation of a polymer P having amide and ester groups in the solid state of aggregation, in a first step (a) a homo- or copolymer P1 of (meth)acrylic acid, itaconic acid or crotonic acid being reacted with at least one monohydroxy compound E at a temperature up to 200.degree. C. to give a polymer P2, so that anhydride groups form in addition to ester groups, in a second step (b) the polymer P2 prepared in step (a) being cooled to below 60.degree. C. so that the polymer P2 is present in the solid state of aggregation or as supercooled melt, and in a third step (c) the polymer P2 having anhydride groups and present in the solid state of aggregation or as supercooled melt being amidated with at least one amine compound A at temperatures below 60.degree. C., the amine compound A used in the third step (c) being present in the solid state of aggregation or on or in a solid carrier material.