The present invention relates to the use of water soluble or water dispersible polymers containing carboxyl groups, optionally in latent form, and side-chains of general formula (I): -X-Y-[-O-(-Alk-O)n-R]k as additives in mineral building materials, wherein X, Y, Alk, R, n and k have the meanings cited in Claim 1. Said polymers can be obtained by polymerizing ethylenically unsaturated monomers in the presence of compounds containing phosphorus and, optionally, by additional polymer-analogous transformation. The invention further relates to the production of said polymers and the use thereof. Also described are polymers, which can be obtained by polymerizing aromatic vinyl compounds, olefins, cycloolefins and/or dienes, as D monomers and anhydrides of ethylenically unsaturated dicarboxylic acids as E monomers, and which can be used both as parent compounds for the above-mentioned polymers and as additives for mineral building materials.00000