Abstract We study fretting wear due to superimposed oscillations in the normal and tangential directions with respect to the contact plane (dual mode fretting wear). In the limit of infinite time, the profile of the indenter tends to a limiting shape, which does not change further. For axisymmetric profiles, the limiting shape is found analytically for the general case of two different frequencies and amplitudes of oscillations in normal and tangential direction. The dependence of worn volume on the frequency ratio is strongly singular showing sharp minima for small rational ratios of frequencies. For the special case of coinciding frequencies, the fretting process was studied both analytically and experimentally. Comparison of experimental results with theoretical predictions showed a good qualitative and quantitative agreement (discrepancy of the order of experimental noise).