Abstract. We have measured Ti L_2,3-edge X-ray magnetic circular dichroism (XMCD) spectra of Co doped anatase TiO₂ (Co_0.05Ti_0.95O₂), where nonzero XMCD spectra have been observed even at Ti L_2,3-edge. In order to understand the reason why the XMCD signals are observed at Ti L_2,3-edge, we have applied the relativistic multiple-scattering approach to the analyses of the observed XMCD spectra. The results show that the Ti L_2,3-edge XMCD spectra are dominated by the spin-dependent exchange scatterings on the spin-polarized Co sites. We find a good agreement with the observed L₃ XMCD spectra. The calculated XMCD spectra are rather sensitive to the spin moment on the X-ray absorbing Ti. We conclude that the spin moment on Ti site is very small and antiparallel to that on Co. The calculated results also show that the observed Ti L_2,3-edge XMCD signals arise from the Ti atoms within about 4 Å from spin-polarized Co atoms.