Process to monitor and control the quality of rolled products from hot-rolled processes which produce products such as sheets, rods, etc., from input stock such as slabs, billets, etc. The process estimates in advance the expected material properties of the end product at each step of the hot-rolling production process. The process further provides that conditions, such as temperature, reduction depth, etc., are detected on-line throughout the entire rolling process and from the values obtained, via interrelated physical—metallurgical and/or statistical models describing the whole rolling process, the mechanical/technical material properties to be expected, particularly the yield point, the tensile strength and the breaking elongation point of the rolled product, are calculated. On-line detection of the actual and momentary production conditions is necessary to allow the material properties to always be estimated in advance.