  We discuss the non-abelian duality procedure for groups which do not act
freely. As an example we consider Taub-NUT space, which has the local isometry
group $SU(2) \otimes U(1)$. We dualise over the entire symmetry group as well
as the subgroups $SO(3)$ and $U(1)$, presenting unusual new solutions to low
energy string theory. The solutions obtained highlight the relationship between
fixed points of an isometry in one solution and singular points in another. We
also find the interesting results that, in this case, the $U(1)$ and $SO(3)$
$T$-duality procedures commute with each other, and that the extreme points of
the $O(1,1)$ duality group for the time translations have special significance
under the $SO(3)$ T-duality.
