Polyamide foams which inhibit the spread of fires are obtained by mixing (i) a liquid isocyanate component which contains at least one polyisocyanate, wherein the molar ratio of aromatic isocyanate groups to the sum of aromatic and aliphatic isocyanate groups is at least 60 mol.%, with (ii) at least one liquid isocyanate-reactive component which contains a reactive diluent that comprises (a) a chain-extending and/or crosslinking reactive diluent selected from aliphatic branched C24-66-polycarboxylic acids, alicyclic C24-66-polycarboxylic acids, and partial esterns of polycarboxylic acids withat least two unesterified carboxyl groups and/or b) a chain-terminating reactive diluent selected from aliphatic branched C24-66-monocarboxylic acids, alicyclic C24-66-monocarboxylic acids, and partial esters of polycarboxylic acids with an unesterified carboxyl group, and (iii) optionally a solid isocyanate-reactive component. The liquid isocyanate-reactive component and/or the solid isocyanate-reactive component comprises an aromatic C8-18-polycarboxylic acid and/or an anhydride thereof. Reactive diluents are dimeric fatty acids or trimeric fatty acids which are optionally hydrogenated. Thefoams are suitable for filling cavities in mining, tunnel construction, underground engineering or for obtaining oil and gas as a fire protection foam, heat damping, or acoustic damping.