Disclosed is a steam generator in which a continuous evaporating heating area is disposed within a heating gas duct that is penetrated in a nearly horizontal direction by a heating gas. Said continuous evaporating heating area comprises a number of steam-generating pipes that are connected in parallel and are penetrated by a flowing medium and is configured such that a steam-generating pipe which is heated more than another steam-generating pipe of the same continuous evaporating heating area has a higher throughput of the flowing medium than said other steam-generating pipe. The aim of the invention is to create a steam generator which provides a particularly high degree of stability of flow during operation of the continuous evaporating heating area while keeping the structural complexity and design comparatively simple. Said aim is achieved by means of a discharge collector which is mounted downstream of the steam-generating pipes of the continuous evaporating heating area on the side of the flowing medium, and the longitudinal axis of which is located essentially parallel to the direction of the heating gas.