We report a dielectric anomaly in several perovskites at intermediate frequencies 10\ensuremath{\le}f\ensuremath{\le}${10}^{7}$ Hz in the temperature range 400 \ifmmode^\circ\else\textdegree\fi{}C \ensuremath{\le}T\ensuremath{\le}800 \ifmmode^\circ\else\textdegree\fi{}C. We have found this dielectric maximum in more than 100 samples of various shapes and textures. This anomaly is shown to arise from a Debye dielectric dispersion that slows down following an Arrhenius law. We have established a link between this dielectric relaxation and the conductivity. We propose that it can be achieved through a space-charge model that quantitatively agrees with the experimental results in the lower temperature range.