Field dependence of dielectric properties of barrier anodic oxide films on Al foil was measured using a small amplitude ac signal with dc bias voltage. The dc field was as high as 85% of the oxide formation field. Amorphous and crystalline oxides up to 700 nm thick were examined. An oxide is either a linear or nonlinear ͑field-dependent͒ dielectric, depending on its thermal history. Oxide formed and measured at room temperature, i.e., usual laboratory conditions, is a linear dielectric, capacitance ͑C͒ and dissipation factor ͑DF͒ exhibit no field dependence. Exposure to elevated temperature during growth, typical for commercial capacitor foil, produces a nonlinear dielectric. Both C and DF increase with field, but the increase in DF is much greater, such that at the highest field some commercial oxides have DF 50% larger than at zero bias voltage. C has quadratic dependence on field, but DF has either linear or quadratic dependence, determined by oxide thickness. Subsequent growth of a small additional thickness of oxide at room temperature removes the field dependence. Nonlinear properties of amorphous and crystalline oxides are qualitatively the same. Field dependence of dielectric properties is discussed with reference to oxide structure.A linear dielectric has permittivity independent of the applied field. ͓The complex permittivity ͑ * ͒ has a real component, Ј, the dielectric constant, and imaginary component, Љ, the dielectric loss.͔ Both tantalum oxide 1 and niobium oxide 2 films exhibit electro-optic and electrostrictive behavior such that the refractive index decreases with field, and the film thickness increases. The fractional changes are of the order 10 −3 at fields close to that for oxide growth. There are a few reports for anodic oxides of nonlinear behavior at frequencies well below the optical range, e.g., 1 kHz. Kliem and Schumacher 3 reported that for 50 nm alumina films measured at a field of 5 ϫ 10 8 V m −1 , Ј increased by ϳ5% and Љ increased by ϳ50%, in comparison to values at zero bias voltage. 3 Oxide growth conditions were not described for this work, but 5 ϫ 10 8 V m −1 is probably ϳ60-70% of the growth field. Wyatt 4,5 studied Ta 2 O 5 films at low temperature and found C decreased ϳ1% when a field of order 10 8 V m −1 is applied. He reported field dependence of dissipation factor ͑DF͒ but gave few details. We have reported some field-dependent dielectric properties of aluminum anodic oxide films at the limited conditions, 1-30 Hz, large field modulation, under the application of bipolar constant current pulses. 6,7 These reports of nonlinear behavior at frequencies Յ1 kHz show changes one to two orders larger than in the optical range, and of different origin.Our interest in low-frequency nonlinear effects is prompted by power electronics applications for Al electrolytic capacitors in circuits for speed control of ac motors. 8,9 The capacitor sustains a high dc bias voltage modulated by an ac voltage, and this drives a large ripple current between the capacitor plates. The ac voltage a...