  We investigate perturbative aspects of gravity with a general F(R)
Lagrangian, as well as nonperturbative dilatonic solutions. For the first part,
we are interested in stability and the definition of asymptotic charges. The
main result of this study is that, while generic F(R) theories are stable under
metric perturbations, they are expected to show instabilities against curvature
perturbations when the Lagrangian includes 1/R terms. For the second part, one
is interested on exact solutions, and we explicitly construct kink-like
solutions of the Liouville type for the dilaton field for F(R) having the form
R+\gamma R^n, in two and in four dimensions.
