  We present first results of the non-linear evolution of rotating relativistic
stars obtained with an axisymmetric relativistic hydrodynamics code in a fixed
spacetime. As initial data we use stationary axisymmetric and perturbed
configurations. We find that, in order to prevent (numerical) angular momentum
loss at the surface layers of the star a high-resolution grid (or a numerical
scheme that retains high order at local extrema) is needed. For non-rotating
stars, we compute frequencies of radial and non-radial small-amplitude
oscillations, which are in excellent agreement with linear normal mode
frequencies computed in the Cowling approximation. As a first application of
our code, quasi-radial modes of rapidly rotating relativistic stars are
computed. By generalizing our numerical code to 3-D, we plan to study the
evolution and non-linear dynamics of toroidal oscillations (r-modes) of rapidly
rotating neutron stars, which are a promising source of gravitational waves.
