Changes in the topology of anodic oxides grown on a two-phase Zr-2.5Nb alloy have been observed with atomic force microscopy (AFM) as a function of oxide thickness. For thin films grown with relatively low anodization voltages, the oxide formed over the beta-Zr phase of the alloy appeared rougher and protruded above that grown over the more abundant a phase. When the anodization voltage was similar to80 V. the average thickness of the anodic film reached similar to200-300 nm, and the oxide formed over the a phase changed abruptly to become as rough as that formed initially above the P regions. Area-scale fractal dimensions have been calculated from the AFM measurements for these oxides as a function of anodization voltage. These values agree remarkably well with 'surface' fractal dimensions inferred from analyses of electrochemical impedance spectra in which the oxide is treated as the dielectric in a fractal capacitor. (C) 2002 Elsevier Science B.V. All rights reserved.