  A class of Modified Gravity Models, consisting of inverse powers of linear
combination of quadratic curvature invariants, is studied in the full parameter
space. We find that singularity-free cosmological solutions, interpolating
between an almost-Friedmann universe at Big Bang Nucleosynthesis and an
accelerating universe today, exist only in a restricted parameter space.
Furthermore, for all parameters of the models, there is an unstable scalar mode
of the gravitational field. Therefore we conclude that this class of Modified
Gravity Models is not viable.
