  Perturbations of rotating relativistic stars can be classified by their
behavior under parity. For axial perturbations (r-modes), initial data with
negative canonical energy is found with angular dependence $e^{im\phi}$ for all
values of $m\geq 2$ and for arbitrarily slow rotation. This implies instability
(or marginal stability) of such perturbations for rotating perfect fluids. This
low $m$-instability is strikingly different from the instability to polar
perturbations, which sets in first for large values of $m$. The timescale for
the axial instability appears, for small angular velocity $\Omega$, to be
proportional to a high power of $\Omega$. As in the case of polar modes,
viscosity will again presumably enforce stability except for hot, rapidly
rotating neutron stars. This work complements Andersson's numerical
investigation of axial modes in slowly rotating stars.
