By definition, an N-dimensional positive-definite inhomogeneous metric is not invariant under any N-parameter, simply-transitive continuous group of motions. Nonetheless, it is possible to construct a group (simply-transitive and of N parameters) that comes closest to leaving the given metric invariant. We call this group the approximate symmetry group of the metric. In an earlier paper, we described a technique for constructing the approximate symmetry group of a given metric. Here, we briefly review that technique and then present some examples of its application. All two-dimensional metrics are analyzed, and simple criteria are given for determining their approximate symmetry groups. Three three-dimensional metrics are investigated: the invariant hypersurfaces of the Kantowski–Sachs space–times and two families of hypersurfaces in the Gowdy T3 space–times. The approximate symmetry group of the former is found to be of Bianchi Type I and those of the latter may be I or VI0. Defining, via our technique, a measure I of the magnitude of a metric’s inhomogeneity, we study the time dependence of I for the hypersurfaces in the Gowdy metric. We find it is possible in some cases for these hypersurfaces to approach homogeneity (I→0) both in the asymptotic future and near the initial singularity. Finally, we constant a homogeneous background metric for these hypersurfaces.