The invention relates to a method and a device for hot sealing multiple plies of a laminate from which, in particular, gable top packaging for holding liquid foodstuffs can be produced, wherein the laminate comprises a carrier layer made of electrically non-conductive material, for example cardboard, and a sealing layer made of thermoplastic material, for example polyethylene, on at least one surface of the laminate. Hot sealing in the high-frequency alternating electric field is problematic when the number of plies of the laminate in the sealing region varies. In order to provide a method and a device for hot sealing multiple plies of a laminate in a high-frequency alternating electric field, in which problems due to an excessively great or excessively low introduction of heat into the plies of the laminate that are to be sealed are avoided, it is proposed according to the invention that the alternating electric field is generated by a first lead of the HF voltage supply in a first sub-region (71) of the sealing region (70) and is generated by a second lead of the HF voltage supply, differing from the first lead, in at least a second sub-region (72) of the sealing region (70), so that a different heat distribution is obtained over the sub-regions (71, 72) of the sealing region (70). The different heat distribution in the sub-regions (71, 72) enables a targeted adaptation to the heat requirement demanded in the respective sub-regions (71, 72).