Composite material (10) comprises a substrate (1) and a chemically, mechanically, physically, catalytically and/or optically functional titanium oxide layer (2), applied on at least one side thereof. A titanium oxide layer (2) is deposited on the substrate (1) as a base layer (3), made from TiO.sub.x with an oxygen content of 0.7.ltoreq.x<2, or made from TiO.sub.x(OH).sub.y with an oxygen content of 0.5.ltoreq.x<2 and a hydroxide content of 0.ltoreq.y<0.7 and an upper layer (4) of amorphous and/or crystalline TiO.sub.2 applied to said base layer (3). In a first method variation, firstly a base layer (3) of TiO.sub.x with an oxygen content of 0.7.ltoreq..times.<2 is reactively or non-reactively deposited, then, through an increase in the oxygen content, the process pressure, the capacity and/or the substrate temperature, an upper layer (4) of amorphous and/or crystalline TiO.sub.2 is deposited. In a second method variation, firstly a base layer (3) of TiO.sub.x with an oxygen content of 0.7.ltoreq.x<2 is reactively or non-reactively deposited and then post-oxidized on the surface by means of an electrochemical, thermal and/or plasma process, until the base layer (3) is converted into amorphous or crystalline TiO.sub.2 at least partly in an upper layer (4).