Abstract: Method for converting two-dimensional or three-dimensional sheet structures consisting of polyacrylonitrile fibres or substantially of polyacrylonitrile fibres, such as woven fabrics, layered materials, knitted fabrics, felts, or non-woven fabrics, into the thermally stabilized but non-carbonized state, by means of an oxygen-containing or oxygen-yielding gas flowing through the respective sheet fibre structure. This gas or gas mixture is used as a medium for the temperature control in the sheet fibre structure and as a means for supplying the oxygen carrier and also removing the gaseous reaction products. Temperature and flow velocity of the gas/gas mixture are matched to the stabilization characteristic of the respective sheet fibre structure and are controlled precisely. The device used for carrying out the method consists of a furnace (23) which consists of at least one chamber, through which furnace a web of the sheet fibre structure (18) is moved continuously.