The invention relates to halogen-free, flame-retarded polymer foams, in particular, polystyrol particulate foams made from expanded polystyrene (EPS) or extruded polystyrene foam sheets (XPS), containing a phosphorous compound as flame-retarding agent of general formula (I), where R1, R2 and R3 independently = H, substituted or non-substituted C1-C15 alkyl, substituted or non-substituted C1-C15 alkenyl, substituted or non-substituted C3-C8 cycloalkyl, substituted or non-substituted C6-C18 aryl or substituted or non-substituted C7-C30 alkylaryl, or the product from hydrolysis or a metal salt of a phosphorus compound of general formula (I) and a method for production thereof.