Emulsion polymers obtainable by emulsifying a mixture consisting ofA) 5 to 95 % by weight of at least one monomer from the series consisting of acrylonitrile, methacrylonitrile, optionally substituted styrene, vinyl carboxylate andB) 5 to 95 % by weight of acrylic and/or methacrylic esters,the sum of components A)+B) being 100% by weight, in the presence of an aqueous solution or dispersion of an anionically modified polyurethane, preferably containing --SO.sub.3.sup.-Me.sup.+ and/or -COO.sup.- Me.sup.+ groups (Me.sup.+ =cation, preferably H.sup.+, Na.sup.+, K.sup.+, Li.sup.+, NH.sub.4.sup.+ or a substituted ammonium ion), and subjecting the resulting emulsion to a polymerization initiated by free radicals.The emulsion polymers produced are preferably used as surface sizing agents for paper.