  We study the strong gravity regime in viable models of so-called f(R) gravity
that account for the observed cosmic acceleration. In contrast with recent
works suggesting that very relativistic stars might not exist in these models,
we find numerical solutions corresponding to static star configurations with a
strong gravitational field. The choice of the equation of state for the star is
crucial for the existence of solutions. Indeed, if the pressure exceeds one
third of the energy density in a large part of the star, static configurations
do not exist. In our analysis, we use a polytropic equation of state, which is
not plagued with this problem and, moreover, provides a better approximation
for a realistic neutron star.
