A method is proposed for sterilizing packaging material of plastic, cardboard or combinations of the two, in particular for sterilizing preshaped packaging containers intended for receiving acidic products. In this method, damage to the packaging material or the packaging apparatus is to be avoided because of the mild thermal treatment involved. By subjecting the surface to be treated to a flow of a moist mixture of water vapor and air at a temperature of from 80.degree. to 140.degree. C. and having a moisture content of from 5 to 50%, sufficiently high degrees of sterility for the sterile packaging of acidic food products are attainable within relatively short treatment periods.