The invention relates to the marking of a material (18) with identifier marks (16), the material thus marked, and verification of the genuineness of a product on the basis of the marks. In accordance with the invention, an optical brightener is incorporated in the material (18), and marking is performed by reducing the brightness of the material at a selected location by directing local heating to this location, the mark (16) thus produced appearing with a darker shade than its environment in ultraviolet light (20). The marking is based on partial or complete destruction of the brightening effect of the optical brightener under heating. The invention is suitable for providing e.g. coated paper and board containing an optical brightener with identifier marks for preventing falsifications.