Transparent pure and Cu-doped (2.5, 5 and 10 at.%) anatase TiO₂ thin films were grown by pulsed laser deposition technique on LaAlO₃ substrates. The samples were structurally characterized by X-ray absorption spectroscopy and X-ray diffraction. The magnetic properties were measured using a SQUID. All films have a FM-like behaviour. In the case of the Cu-doped samples, the magnetic cycles are almost independent of the Cu concentration. Cu atoms are forming CuO and/or substituting Ti in TiO₂. The thermal treatment in air promotes the CuO segregation. Since CuO is antiferromagnetic, the magnetic signals present in the films could be assigned to Cu substitutionally replacing cations in TiO₂.