We report on relaxation of trapped photocarriers in the layered perovskite ${\mathrm{Nd}}_{2}$${\mathrm{Ti}}_{3}$${\mathrm{O}}_{9}$ which contains a high density of oxygen vacancies. It is shown that after termination of cw illumination a nonexponential relaxation of photocreated carriers with an increasingly slow rate of decay is observed. This phenomenon, also named persistent photoconductivity, only occurs when light is absorbed at the sample surface and under vacuum; in the presence of air a very fast return to equilibrium is observed. Typical photocurrent (${\mathit{i}}_{\mathit{p}}$) decays recorded after visible or uv excitation and their variations with temperature are reported. In all cases we found that the instantaneous lifetime follows a power-law time dependence: ${\mathrm{\ensuremath{\tau}}}_{\mathrm{inst}}$= ${\mathit{i}}_{\mathit{p}}$(t)/\ensuremath{\Vert}${\mathit{di}}_{\mathit{p}}$/dt\ensuremath{\Vert} \ensuremath{\propto}${\mathit{t}}^{\mathrm{\ensuremath{\alpha}}}$ (01), indicative of dispersive behavior. Photocurrent decays could be fitted with great accuracy, for times up to 24 h, to a stretched exponential relaxation law: ${\mathit{i}}_{\mathit{p}}$(t)=${\mathit{i}}_{\mathit{p}}$(0)exp-(t/\ensuremath{\tau}${)}^{\mathrm{\ensuremath{\beta}}}$, with \ensuremath{\beta}= 1-\ensuremath{\alpha}. On this basis it is assumed that randomly distributed oxygen vacancies acting as trapping centers for electrons are submitted to dispersive diffusion, which thus controls carrier recombination. The distribution of localized states in the gap is discussed in terms of a random distribution of oxygen vacancies. An Urbach-type edge between 2.20 and 2.75 eV below ${\mathit{E}}_{\mathit{c}}$ is revealed by the photocurrent excitation spectrum, whereas an exponential distribution of trapping centers close to ${\mathit{E}}_{\mathit{c}}$ of width \ensuremath{\sim} 60 meV is deduced from the temperature dependence of \ensuremath{\beta}. The observed complex variations of the relaxation time \ensuremath{\tau} with temperature and pressure are linked to the presence of chemisorbed species in oxygen vacancies and rationalized in terms of oxygen coverage of the sample surface. \textcopyright{} 1996 The American Physical Society.