The sealing device for packages that includes a control unit, a sealing station, an unwinder for a film web, a cutting device provided upstream of the sealing station and used for producing film sections of the film web, a film feed device for feeding the film sections to the sealing station, a conveying device for conveying packages into the sealing station. Preferrably, the packages include food packed in a gas-tight manner. Further, the sealing station may comprise upper and lower sealing elements that are configured for clamping the package and the film section in common between the lower and upper sealing elements and for sealing the film section onto the package. The sealing device may also include the sealing elements being adapted to be synchronously moved along with the continuously moving package during the sealing process.