A process for producing fiber webs, comprising spraying one or more aqueous binder formulations containing at least one vinyl ester polymer, (meth)acrylic ester polymer, or mixtures thereof, and, in a separate step, spraying one or more aqueous silicone formulations containing one or more polysiloxanes onto the surface of an airlaid nonwoven, wherein the fibers of the airlaid nonwoven have a length of 0.5 μm to 20 mm and the fiber webs comprise natural fiber materials selected from the group consisting of cellulose fibers, wherein the vinyl ester polymers are selected from the group comprising copolymers of one or more vinyl esters with 1 to 50 wt% of ethylene; copolymers of one or more vinyl esters with 1 to 50 wt% of ethylene and 0.5 to 10.0 wt% of postcrosslinking monomers; copolymers of vinyl acetate with 1 to 50 wt% of ethylene and 1 to 50 wt% of one or more further comonomers from the group of vinyl esters having 1 to 13 carbon atoms in the carboxylic acid moiety and optionally 0.5 to 10.0 wt% of postcrosslinking monomers; copolymers of one or more vinyl esters, 1 to 50 wt% of ethylene and 1 to 60 wt% of (meth)acrylic ester of branched or unbranched alcohols having 1 to 15 carbon atoms and optionally 0.5 to 10.0 wt% of postcrosslinking monomers; copolymers with 30 to 75 wt% of vinyl acetate, 1 to 30 wt% of vinyl laurate or vinyl ester of an alpha-branched carboxylic acid having 9 to 13 carbon atoms and 1 to 30 wt% of (meth)acrylic ester of branched or unbranched alcohols having 1 to 17 carbon atoms, which additionally contain 1 to 40 wt% of ethylene and optionally 0.5 to 10.0 wt% of postcrosslinking monomers; copolymers with one or more vinyl esters, 1 to 50 wt% of ethylene and 1 to 60 wt% of vinyl chloride and optionally further vinyl esters and/or (meth)-acrylic esters and optionally 0.5 to 10.0 wt% of postcrosslinking monomers; wherein the recitations in wt% add up to 100 wt% in each case. wherein the fibers of the airlaid nonwoven have a length of 0.5 μm to 20 mm and the fiber webs comprise natural fiber materials selected from the group consisting of cellulose fibers, wherein the vinyl ester polymers are selected from the group comprising copolymers of one or more vinyl esters with 1 to 50 wt% of ethylene; copolymers of one or more vinyl esters with 1 to 50 wt% of ethylene and 0.5 to 10.0 wt% of postcrosslinking monomers; copolymers of vinyl acetate with 1 to 50 wt% of ethylene and 1 to 50 wt% of one or more further comonomers from the group of vinyl esters having 1 to 13 carbon atoms in the carboxylic acid moiety and optionally 0.5 to 10.0 wt% of postcrosslinking monomers; copolymers of one or more vinyl esters, 1 to 50 wt% of ethylene and 1 to 60 wt% of (meth)acrylic ester of branched or unbranched alcohols having 1 to 15 carbon atoms and optionally 0.5 to 10.0 wt% of postcrosslinking monomers; copolymers with 30 to 75 wt% of vinyl acetate, 1 to 30 wt% of vinyl laurate or vinyl ester of an alpha-branched carboxylic acid having 9 to 13 carbon atoms and 1 to 30 wt% of (meth)acrylic ester of branched or unbranched alcohols having 1 to 17 carbon atoms, which additionally contain 1 to 40 wt% of ethylene and optionally 0.5 to 10.0 wt% of postcrosslinking monomers; copolymers with one or more vinyl esters, 1 to 50 wt% of ethylene and 1 to 60 wt% of vinyl chloride and optionally further vinyl esters and/or (meth)-acrylic esters and optionally 0.5 to 10.0 wt% of postcrosslinking monomers; wherein the recitations in wt% add up to 100 wt% in each case.