A process for the preparation of foamed plastics materials based on polyisocyanate polyaddition products by the reaction of isocyanates with isocyanate-reactive compounds in the presence of catalysts and, optionally, auxiliaries and/or additives, wherein i) isocyanates having isocyanurate and/or biuret structures are used, the isocyanate-reactive compounds used are ii) at least one diol and/or polyol having a molecular weight of from 400 to 8000 and containing at least 50% of primary hydroxyl groups based on all of the hydroxyl groups present in the compound, iii) at least one compound having at least one primary amine group, and diols and/or triols having molecular weights of less than 400 are optionally used as chain-extending and/or crosslinking agents, the reaction being carried out in the presence of iv) at least one tertiary amine acting as catalyst and/or v) at least one metal salt acting as catalyst and vi) water.