Many studies have used the frozen flux hypothesis to estimate core flow from geomagnetic secular variation (SV). Part of the flow remains indeterminate without some additional constraint. A theorem of Voorhies and Backus states that steady flows can be determined uniquely. Frozen flux requires the time scale of SV, &tgr;B, to be much shorter than the diffusion time, &tgr;D, and the steady motion theorem requires the time scale for change in flow, &tgr;V, be much longer than &tgr;B. Here we argue we must also have &tgr;V≪&tgr;D because truly steady flow will eventually lead to a steady equilibrium magnetic field and no SV. We illustrate the difficulty by a numerical example with a prescribed steady flow at the top of the core for which frozen flux inversions never yield the correct velocity. Core motions derived using the steady motions theorem may be grossly in error. ¿ American Geophysical Union 1996