Experimental results related to the photoactivated dc conductance of anatase TiO2 nanotubular arrays (aTNTAs) under pulsed irradiation by a laser light inside and outside the fundamental absorption band are presented. It is found that the mobility and diffusion coefficients of charge carriers in the examined aTNTA are extremely low due to a strong charge-phonon coupling, abundance of shallow traps, and hopping conductivity between adjacent nanotubes. We consider that the confining electric field appeared within the array structure due to the difference in the local concentrations of excess electrons and holes at large values of the dc conductance suppresses the drift current. In this case, the dc conductance of such aTNTAs is mainly matured by the diffusion of mobile carriers. A recurrent kinetic model for evolution of the dc conductance of aTNTAs under laser irradiation has been proposed to interpret the experimental results.