The present invention relates to silo covers comprising at least two layers, wherein an inner first layer facing the silo is a single- or multi-ply plastic film having oxygen permeability according to DIN 53380-3 at 23° C. and 50% relative humidity of no more than 500 cm3/(m2 d bar) and a water vapor transmission rate according to ISO 15106-3 at 23 ° C. and 85% relative humidity of at least 5 g/(m2 d), and in at least one ply in total contains at least 50% by weight of one or more materials from the group comprising polyamide, copolyamide, polyester, copolyester, polyethylene vinyl alcohol, polyvinyl alcohol and mixtures thereof, and at least one second layer, which is located on top of the inner layer and is separate from the inner layer, or easy to separate therefrom, or self-separating on the silo, composed of at least 70% by weight of materials from the group comprising polyethylene, polypropylene, copolymers of ethylene and other vinyl monomers, and copolymers made of propylene and other vinyl monomers.