A composite, comprising from 30 to 90% by weight of natural fibers, from 9 to 69% by weight of at least one thermoplastic polymer, from 1 to 10% by weight of at least one random copolymer whose molar mass M n is up to at most 20 000 g/mol, obtainable via copolymerization of (a) from 60 to 98% by weight of ethylene, (b) from 2 to 40% by weight of at least one reactive comonomer, selected from ethylenically unsaturated C 3 -C 10 monocarboxylic acids, ethylenically unsaturated C 4 -C 10 dicarboxylic acids or their anhydrides, epoxy esters of ethylenically unsaturated C 3 -C 10 monocarboxylic acids, comonomers of the general formula I in which the definitions of the variables are as follows: R 1 is selected from hydrogen and unbranched and branched C 1 -C 10 -alkyl, R 2 is selected from hydrogen and unbranched and branched C 1 -C 10 -alkyl, R 3 is identical or different and is selected from hydrogen and unbranched and branched C 1 -C 10 -alkyl and C 3 -C 12 -cycloalkyl, where two radicals R 3 can have been bonded to one another to form a 3-10-membered ring, X is selected from oxygen, sulfur and N-R 4, R 4 is selected from unbranched and branched C 1 -C 10 -alkyl, A 1 is a divalent group selected from C 1 -C 10 -alkylene, C 4 -C 10 -cycloalkylene, and phenylene, and (c) optionally at least one further comonomer. from 30 to 90% by weight of natural fibers, from 9 to 69% by weight of at least one thermoplastic polymer, from 1 to 10% by weight of at least one random copolymer whose molar mass M n is up to at most 20 000 g/mol, obtainable via copolymerization of (a) from 60 to 98% by weight of ethylene, (b) from 2 to 40% by weight of at least one reactive comonomer, selected from ethylenically unsaturated C 3 -C 10 monocarboxylic acids, ethylenically unsaturated C 4 -C 10 dicarboxylic acids or their anhydrides, epoxy esters of ethylenically unsaturated C 3 -C 10 monocarboxylic acids, comonomers of the general formula I in which the definitions of the variables are as follows: R 1 is selected from hydrogen and unbranched and branched C 1 -C 10 -alkyl, R 2 is selected from hydrogen and unbranched and branched C 1 -C 10 -alkyl, R 3 is identical or different and is selected from hydrogen and unbranched and branched C 1 -C 10 -alkyl and C 3 -C 12 -cycloalkyl, where two radicals R 3 can have been bonded to one another to form a 3-10-membered ring, X is selected from oxygen, sulfur and N-R 4, R 4 is selected from unbranched and branched C 1 -C 10 -alkyl, A 1 is a divalent group selected from C 1 -C 10 -alkylene, C 4 -C 10 -cycloalkylene, and phenylene, and (c) optionally at least one further comonomer. (a) from 60 to 98% by weight of ethylene, (b) from 2 to 40% by weight of at least one reactive comonomer, selected from ethylenically unsaturated C 3 -C 10 monocarboxylic acids, ethylenically unsaturated C 4 -C 10 dicarboxylic acids or their anhydrides, epoxy esters of ethylenically unsaturated C 3 -C 10 monocarboxylic acids, comonomers of the general formula I in which the definitions of the variables are as follows: R 1 is selected from hydrogen and unbranched and branched C 1 -C 10 -alkyl, R 2 is selected from hydrogen and unbranched and branched C 1 -C 10 -alkyl, R 3 is identical or different and is selected from hydrogen and unbranched and branched C 1 -C 10 -alkyl and C 3 -C 12 -cycloalkyl, where two radicals R 3 can have been bonded to one another to form a 3-10-membered ring, X is selected from oxygen, sulfur and N-R 4, R 4 is selected from unbranched and branched C 1 -C 10 -alkyl, A 1 is a divalent group selected from C 1 -C 10 -alkylene, C 4 -C 10 -cycloalkylene, and phenylene, and ethylenically unsaturated C 3 -C 10 monocarboxylic acids, ethylenically unsaturated C 4 -C 10 dicarboxylic acids or their anhydrides, epoxy esters of ethylenically unsaturated C 3 -C 10 monocarboxylic acids, comonomers of the general formula I in which the definitions of the variables are as follows: R 1 is selected from hydrogen and unbranched and branched C 1 -C 10 -alkyl, R 2 is selected from hydrogen and unbranched and branched C 1 -C 10 -alkyl, R 3 is identical or different and is selected from hydrogen and unbranched and branched C 1 -C 10 -alkyl and C 3 -C 12 -cycloalkyl, where two radicals R 3 can have been bonded to one another to form a 3-10-membered ring, X is selected from oxygen, sulfur and N-R 4, R 4 is selected from unbranched and branched C 1 -C 10 -alkyl, A 1 is a divalent group selected from C 1 -C 10 -alkylene, C 4 -C 10 -cycloalkylene, and phenylene, and R 1 is selected from hydrogen and unbranched and branched C 1 -C 10 -alkyl, R 2 is selected from hydrogen and unbranched and branched C 1 -C 10 -alkyl, R 3 is identical or different and is selected from hydrogen and unbranched and branched C 1 -C 10 -alkyl and C 3 -C 12 -cycloalkyl, where two radicals R 3 can have been bonded to one another to form a 3-10-membered ring, X is selected from oxygen, sulfur and N-R 4, R 4 is selected from unbranched and branched C 1 -C 10 -alkyl, A 1 is a divalent group selected from C 1 -C 10 -alkylene, C 4 -C 10 -cycloalkylene, and phenylene, (c) optionally at least one further comonomer.