  We study inhomogeneous cosmological variations in the fine structure
'constant', $\alpha ,$ in Friedmann universes. Inhomogeneous motions of the
scalar field driving changes in $\alpha $ display spatial oscillations that
decrease in amplitude with increasing time. The inhomogeneous evolution quickly
approaches that found for exact Friedmann universes. We prove a theorem to show
that oscillations of $\alpha $ in time (or redshift) cannot occur in Friedmann
universes in the BSBM theories considered here.
