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