  In this contribution one examines the generalization of the $f(R)$ theories
of gravity where one introduces a non-minimal coupling between curvature and
matter. This model has new and interesting features. %, specially concerning
the energy exchange between the matter fields and the curvature. However, as
any modified gravity theories, these may give origin to anomalies which might
turn the theory physically meaningless. In this respect, one undertakes a study
on the energy conditions and the Dolgov-Kawasaki criterion specific of this new
model.
