The dielectric and piezoelectric response of ferroelectric thin films and ceramics was investigated as a function of the driving field amplitude. Detailed analysis of the amplitude and phase angle of the third harmonic of the dielectric displacement and piezoelectrically induced charge shows that the usual phenomenological approach is inadequate to describe experimentally observed field dependence of the dielectric and piezoelectric response. Qualitatively better agreement with experimental data is obtained using Rayleigh relations, suggesting that the observed field dependence of the polarization and piezoelectric charge may be associated with domain-wall displacement in a medium with a random distribution of pinning centers. The results indicate that the mechanism which controls the electromechanical response is very complex, and that it depends on history of samples, preparation conditions, material microstructure and on driving field amplitude.