  We constrain the viable models of Horndeski gravity, written in its
equivalent Generalised Galileon version, by resorting to the Witten positive
energy theorem. We find that the free function $G_3(\phi, X)$ in the Lagrangian
is constrained to be a function solely of the scalar field, $G_3(\phi)$, and
relations among the free functions are found. Other criterion for stability are
also analysed, such as the attractiveness of gravity, the Dolgov-Kawasacki
instability and the energy conditions. Some applications for Cosmology are
discussed
