  Despite the recent excitement over the r-mode instability of rotating stars,
these modes are not yet well-understood for stellar models appropriate to
neutron stars - perfect fluid models in which both the equilibrium and
perturbed configurations obey the same one-parameter equation of state.
  In spherical stars of this kind, r-modes and g-modes form a degenerate
zero-frequency subspace. Rotation splits the degeneracy to zeroth order in the
star's angular velocity $\Omega$, and the resulting modes are generically
hybrids, whose limit as $\Omega\to 0$ is a stationary current with axial and
polar parts. Lindblom and Ipser have recently found these hybrid rotational
modes in an analytic study of the Maclaurin spheroids. This dissertation
studies them in Newtonian stars (both uniform density models and $n=1$
polytropes) and reports a first computation of the hybrid rotational modes of
relativistic stars.
