  This is a progress report on our study of the coupling of first-order radial
and non-radial relativistic perturbations of a static spherical star. Our goal
is to investigate the effects of this coupling on the gravitational wave signal
of neutron stars. In particular, we are looking for the existence of resonances
and parametric amplifications, changes in the damping time of non-radial
oscillations, etc. To that end, we have developed a formalism that introduces
gauge invariant quantities to describe the coupling. Their equations have the
same structure as the equations for first-order non-radial perturbations plus
some source terms, which makes them very appealing for time domain studies.
