  Hierarchical two-planet systems, in which the inner body's semi-major axis is
between 0.1 and 0.5 AU, usually present high eccentricity values, at least for
one of the orbits. As a result of the formation process, one may expect that
planetary systems with high eccentricities also have high mutual inclinations.
However, here we show that tidal effects combined with gravitational
interactions damp the initial mutual inclination to modest values in timescales
that are shorter than the age of the system. This effect is not a direct
consequence of tides on the orbits, but it results from a secular forcing of
the inner planet's flattening. We then conclude that these hierarchical
planetary systems are unlikely to present very high mutual inclinations, at
least as long as the orbits remain outside the Lidov-Kozai libration areas. The
present study can also be extended to systems of binary stars and to
planet-satellite systems.
