Local response signals in scanning nonlinear dielectric microscopy during domain switching in ferroelectric materials were studied. Periodic response signals corresponding to domain switching were observed in single-crystal LiTaO3 samples under alternating bias voltage applications. This approach was subsequently applied to ferroelectric HfO2 films, showing different response signals depending on the film orientation and the conditions of film formation. These results suggest that the proposed method is useful for obtaining detailed information concerning domain switching in the nanoscale region, such as the pinning-site effect, backswitching, and 90° switching.