A device for heat treating metallic webs in-line, in particular for operation with a low-density protective gas, comprises stabilising nozzle systems which stabilise the course of the web and effect heat transfer, primarily by forced convection, in the heating portion and at least in the first portion of cooling. The web is guided in a non-contact process in the treatment portion localized by rollers. The course of the web exhibits a concave curvature (as viewed from above), at least in a partial area in the treatment portion. The area of said concave curvature can be in a fluid which is different from the fluid with which the web is blown in the heating portion and at least in the first portion of the cooling area.