The switching of the sandwich structure ''ferroelectric+thin dielectric layer'' is theoretically studied. The behavior of the remanent polarization, P-r, coercive field, E(c), maximal polarization on the loop, P-s, and the slope of the hysteresis loop at E(c) as a function of both, the relative thickness of the layer (the thickness of the dielectric divided by the thickness of the ferroelectric) and the amplitude of the measuring field, is analyzed. It is shown that the effect of the layer on P-r and the slope at E(c) is qualitatively different from that on E(c) and P-s. As the result of this analysis the set of characteristic features of the sandwich with the variable relative thickness of the dielectric layer have been have formulated. These characteristic features can be used for the identification of the presence of such a dielectric layer using the data on the switching parameters of the system. It is shown that the increase of the coercive field with increasing relative thickness of the dielectric layer, which was considered as an important sign of the presence of the dielectric layer, is not a real property of the sandwich structure but rather an artifact of the approximations which were used in the analysis performed by the previous workers. In fact, E(c) is a decreasing function of the relative thickness of the dielectric layer. (C) 1995 American Institute of Physics.