The dielectric response of La- and Dy- doped BiFeO3 thin films to electric- and magnetic fields was measured at microwave frequencies (up to 12GHz) in a temperature range from 25 °C to 300 °C. Interesting phenomena were observed. Significant oscillations in the C(f) characteristic which were unaffected by the electric field or by elevated temperature but which were dampened by a magnetic field. We also observed ‘N’-type I-V characteristics. A possible explanation for this mesoscopic response is the presence of structural features that cause resonance (e.g. grains, grain-boundaries, domains, domain walls etc), with a contribution strong enough to be averaged by the system. The exact origin of these features is unknown at present.