  We consider the covariant galileon gravity taking into account the third
order and fourth order scalar field Lagrangians L_3(\pi) and L_4(\pi)
consisting of three and four $\pi$'s with four and five derivatives acting on
them respectively. The background dynamical equations are set up for the system
under consideration and the stability of the self accelerating solution is
demonstrated in general setting. We extended this study to the general case of
the fifth order theory. For spherically symmetric static background, we spell
out conditions for suppression of fifth force effects mediated by the galileon
field $\pi$. We study the field perturbations in the fixed background and
investigate conditions for their causal propagation. We also briefly discuss
metric fluctuations and derive evolution equation for matter perturbations in
galileon gravity.
