A strong influence of ferroelectric polarization on d.c. conduction has been observed in PZT thin films with Pt electrodes. It is shown that the current-voltage response taken for measuring times of hundreds of seconds at room temperature is controlled by the crossover from the transient to steady-state conduction regime. In the transient regime the current flowing against the initial direction of the ferroelectric polarization is higher than that flowing in the reverse direction. In the steady-stare regime a current asymmetry of the opposite sense is observed. At elevated temperatures (150-200 degrees C) the asymmetry in both regimes is strongly suppressed. A Maxwell-Wagner relaxation model with ferroelectric and non-ferroelectric capacitors can qualitatively explain the observed phenomena.