The switching kinetics in ferroelectric thin films has been intensively studied during the past decade. It is widely accepted that this kinetics is basically governed by the dynamics of domain coalescence (the Kolmogorov-Avrami-Ishibashi model). This conclusion is mainly supported by fitting the time dependence of the switching currents to that predicted by this model, the fit being typically performed in a 1-2 decade interval of time. The present paper reports on a study of the switching kinetics in modified Pt/Pb(Zr,Ti)O-3/Pt thin films as a function of time and applied voltage, performed in time intervals from 10 ns to 1s. Our experimental data show that both the time and applied field dependences of the switching polarization (when monitored over a wide enough time interval) are in a strong qualitative disagreement with the predictions of the Kolmogorov-Avrami-Ishibashi approach. For the interpretation of our result, an alternative approach is forwarded. In contrast to Kolmogorov-Avrami-Ishibashi approach, we assume that the film consists of many areas, which have independent switching dynamics. The switching in an area is considered to be triggered by an act of the reverse domain nucleation. The switching kinetics is described in terms of the distribution function of the nucleation probabilities in these areas. The developed approach enables a good description of the polarization dynamics in typical ferroelectric thin films for memory applications.