The anodic oxidation of niobium in sulfuric acid electrolyte is studied using a self-nulling ellipsometer to follow the optical changes that occur when the field in the oxide film is switched. The oxide is optically anisotropic with the anodizing field applied, and the degree of anisotropy, the ratio between index changes parallel and transverse to the field, is found to equal 2.2 by a procedure that requires consistency from the analysis of field-switching transients for a wide range of oxide film thicknesses. The film thickness increases and its refractive index values decrease when the field is applied. The dependences are not the parabolic dependences predicted by the theory of electrostriction, and the significance of this finding is discussed. Although the galvanostatic charge:discharge transients that are used to study the changes in the lowfrequency dielectric constant exhibit significant hysteresis, they show that the decrease in dielectric constant with increasing field observed at optical frequencies occurs also at low frequencies. The results are compared with the dependence of dielectric constant on field deduced from open-circuit transient analysis, and the significance of the discrepancy is discussed. It is concluded that the possibility that the oxide film has a significantly polar structure remains an open question.The anodic oxides of most valve metals appear to be optically anisotropic during anodization. The uniaxial negative anisotropy disappears when the field is removed from tantalum (1) and niobium (2-4), but substantial anisotropy remains at zero field for vanadium (5) and molybdenum (6). The associated changes in the low-frequency dielectric constant are in the same direction as at optical frequency, and the fractional changes are considerably larger at low frequency. The thickness of the oxide film is found to increase when the field is applied, and the change is of about the magnitude r.equired by the Clausius-Mossotti relation to account for the dielectric constant changes.The changes in film thickness and dielectric constant are thought to be due to electrostriction, the universal second-order effect which couples strain and field in nonpolar materials. In the theory of electrostriction, the dielectric constant depend~ on strain in much the same way ,as in the Clausius-Mossotti relation, and the sign of the electrostrictive coefficient determines both how the dielectric constant depends on the strain and how the strain depends on the field. When we compare the experimental results with the theory, we see that it is possible to fit the strain data by choosing a sign for the electrostrictive coefficient.that is opposite to the sign in the Clausius-Mossotti relation, but neither sign can fit the dielectric constant data. If the dielectric constant data are valid, the theory can be shown to violate energy conservation (7), and it must either be modified to make the dielectric constant an explicit function of the field, or the oxide films must be assumed to be polar. Since it is the behav...