  Several f(R) modified gravity models have been proposed which realize the
correct cosmological evolution and satisfy solar system and laboratory tests.
Although nonrelativistic stellar configurations can be constructed, we argue
that relativistic stars cannot be present in such f(R) theories. This problem
appears due to the dynamics of the effective scalar degree of freedom in the
strong gravity regime. Our claim thus raises doubts on the viability of f(R)
models.
