  We investigate how the variation of the obliquity (the axial tilt) of a
hypothetical exo-Earth is effected by the presence of a satellite, an exo-Moon.
Namely, we study analytically and numerically how the range of obliquity of the
exo-Earth changes if an exo-Moon is added to a system comprised of exo-Sun,
exo-Earth and exo-planets. We say that the impact of the exo-Moon is
stabilising if upon the addition of the exo-Moon the range of obliquity
decreases, while we call the impact destabilising if the range increases as the
exo-Moon is added to the system. The problem is considered in a general setup.
The exo-Earth is assumed to be rigid, axially symmetric and almost spherical,
the difference between the largest and the smallest principal moments of
inertia being a small parameter of the problem. Assuming the orbits of the
celestial bodies to be quasiperiodic, we apply time averaging to study rotation
of the exo-Earth at times large compared to the respective periods.
Non-resonant frequencies are assumed. We identify a class of systems for which
we prove analytically that the impact of the exo-Moon is stabilising and a
class where it is destabilising. We also investigate numerically how the impact
of the exo-Moon in a particular system comprised of a star and two planets
varies on modifying the geometry of the orbits of the exo-Moon and the second
planet and the initial obliquity.

Earth and Planetary Astrophysics