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-dependent) dielectric, depending on its thermal history. Oxide formed and measured at room temperature, i.e., usual laboratory conditions, is a linear dielectric, capacitance (C) and dissipation factor (DF) 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.