In this study, perturbation theory has been used for the first time in literature to do small-signal analysis and solution of the memristor-based low-pass and high-pass filters are given using perturbation theory. The time and frequency domain memristor-based filter behaviors are obtained analytically. It has been found that the second harmonic does exist and is dominant and its behavior as a function of frequency is inspected in these filters. The gain responses and the total harmonic distortions of the filters are also given. Results obtained from the perturbation theory are in good agreement with that of numerical simulations and this confirms the accuracy and the performance of the method.