  Recently, in the context of $f(R)$ modified theories of gravity, a new type
of model has been proposed where one directly couples the scalar curvature to
matter. As any model in $f(R)$ theory, there are certain conditions which have
to be satisfy in order to ensure that the model is viable and physically
meaningful. In this paper, one considers this new class of models with
curvature-matter coupling and study them from the point of view of the energy
conditions and of their stability under the Dolgov-Kawasaki criterion.
