  We use latest data from solar system planetary orbital motions to put
constraints on some Galileon-induced precessional effects. Due to the
Vainshtein mechanism, the Galileon-type spherically symmetric field of a
monopole induces a small, screened correction proprtional to \sqrt{r} to its
usual r^-1 Newtonian potential which causes a secular precession of the
pericenter of a test particle. In the case of our solar system, latest data
from Mars allow to constrain the magnitude of such an interaction down to
\alpha <= 0.3 level. Another Galileon-type effect which might impact solar
system dynamics is due to an unscreened constant gradient induced by the
peculiar motion of the Galaxy. The magnitude of such an effect, depending on
the different gravitational binding energies of the Sun and the planets, is \xi
<= 0.004 from the latest bounds on the supplementary perihelion precession of
Saturn.
