  We generalise the Buchdahl-Bondi limit for the case of static, spherically
symmetric, relativistic compact stars immersed in Schwarzschild vacuum in
f(R)-theory of gravity, subject to very generic regularity, thermodynamic
stability and matching conditions. Similar to the case of general relativity,
our result is model independent and remains true for any physically realistic
equation of state of standard stellar matter. We show that an extra-massive
stable star can exist in these theories, with surface redshift larger than 2,
which is forbidden in general relativity. This result gives a novel and
interesting observational test for validity or otherwise of general relativity
and also provides a possible solution to the dark matter problem.
