The invention relates to a method and to a device for drying a fibrous web wherein the traveling fibrous web is acted upon by steam and hot, moist air in the region of a preceding drying zone and is then fed to the preceding drying zone of a downstream drying zone comprising a drying cylinder and a hood allocated thereto. Hot air is taken out of the hood allocated to the drying cylinder of the downstream drying zone. To create at least a portion of the steam for the preceding drying zone, condensate and/or fresh water occurring in the drying cylinder of the downstream drying zone is heated by the hot air taken out of the hood by means of a first heat exchanger. Alternatively or additionally for creating at least a portion of the hot, moist air for the preceding drying zone, the hot air taken out of the hood guided through the first heat exchanger is fed to the preceding drying zone.