The invention provides copolymers of ethylenically unsaturated monomers and of ethylenically functionalized nanoparticles in the form of their aqueous polymer dispersions or water-redispersible polymer powders, obtainable by means of free-radically initiated polymerization in an aqueous medium and, if desired, subsequent drying of the resultant polymer dispersion, ofA) one or more monomers from the group consisting of vinyl esters, (meth)acrylic esters, vinylaromatics, olef ins, 1,3-dienes, vinyl ethers and vinyl halides and, if desired, further monomers copolymerizable therewith, in the presence ofB) at least one particle P having an average diameter of ≦1000 nm, which is functionalized with ethylenically unsaturated, free-radically polymerizable groups, characterized in thatB2) particles P used are one or more from the group of metal oxides and semimetal oxides, and/orB2) particles P used are silicone resins composed of repeating units of the general formula [R4(p+Z)SiO(4−p−Z)/2] (II), where for at least 20 mol % of the respective silicone resin p+z=0, 1 or 3,and where B1) and B2) are each functionalized with one or more α-organosilanes of the general formula (R1O)3−(R2)nSi—(CR32)—X (I), where X is a radical having 2 to 20 hydrocarbon atoms and containing an ethylenically unsaturated group.