  We have computed the eigenfrequencies of f-modes for a constant-rest-mass
sequences of rapidly rotating relativistic inviscid stars in differential
rotation. The frequencies have been calculated neglecting the metric
perturbations (the relativistic Cowling approximation) and expressed as a
function of the ratio between the rotational kinetic energy and the absolute
value of the gravitational energy of the stellar model beta=T/|W|. The zeros
and the end-points of these sequences mark respectively the onset of the
secular instability driven by gravitational radiation-reaction and the maximum
value of beta at which an equilibrium model exists. In differentially rotating
stars the secular stability limits appear at a beta larger than those found for
uniformly rotating stars. Differential rotation, on the other hand, also allows
for the existence of equilibrium models at values of beta larger than those for
uniformly rotating stars, moving the end-point of the sequences to larger beta.
As a result, for some degrees of differential rotation, the onset of the
secular instability for f-modes is generally favoured by the presence of
differential rotation.
