Halogen-free, flame-retardant polymer foams, in particular molded polystyrene foams, composed of expandable polystyrene (EPS) or extruded polystyrene foam sheets (XPS), which comprise, as flame retardant, a phosphorus compound of the general formula (I) where RSUB1/SUB, RSUB2/SUB, and RSUB3/SUB, independently of one another, are H, substituted or unsubstituted CSUB1/SUB-CSUB15/SUB-alkyl, substituted or unsubstituted CSUB1/SUB-CSUB15/SUB-alkenyl, substituted or unsubstituted CSUB3/SUB-CSUB8/SUB-cycloalkyl, substituted or unsubstituted CSUB6/SUB-CSUB18/SUB-aryl, or substituted or unsubstituted CSUB7/SUB-CSUB30/SUB-alkylaryl, or the hydrolysis product or metal salt of a phosphorus compound of the general formula (I), and processes for their production.
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