The invention relates to composite materials, comprising (A) natural fibres, (B) at least one thermoplastic polymer, (C) at least one statistical copolymer with a molecular weight Mn up to a maximum of 20,000 g/mol, obtained by copolymerisation of (a) ethylene, (b) at least one reactive comonomer, selected from (b1) ethylenically-unsaturated C3- C10 monocarboxylic acids, (b2) ethylenically-unsaturated C4-C10dicarboxylic acids or the anhydrides thereof, (b3) epoxy esters of ethylenically-unsaturated C3-C10 monocarboxylic acids, (b4) comonomers of general formula (I) in which the variables are as defined below: R<1> = H, straight- and branched-chain C1-C10 alkyl, R<2> = H, straight- and branched-chain C1-C10 alkyl, R<3> independently = H, straight- and branched-chain C1-C10 alkyl and C3-C12 cycloalkyl, wherein two R<3> groups can be connected together to form a 3- to 10-membered ring, X = O, S or N-R<4>, R<4> = straight- or branched-chain C1-C10 alkyl, A<1> = a divalent group from C1-C10 alkylene, C4-C10 cycyloalkylene and phenylene and (c) optionally at least one further comonomer.