A method for sterilizing containers (2) for receiving food, in particular food in liquid form, in a filling device (14) is described and illustrated, in which a hydrogen peroxide solution (11) is evaporated in an evaporator (12), in which at least one container (2) is subjected to the vaporous hydrogen peroxide in a sterilization zone (3a), and in which the unused portion of the vaporous hydrogen peroxide is extracted at least in part from the sterilization zone (3a). To permit a more economical operation on the whole, it is proposed that the extracted vaporous hydrogen peroxide is at least partially condensed in a condenser (17), and the condensed hydrogen peroxide is added once again to the evaporator (12).