  We investigate the dynamical evolution of hierarchical three-body systems
under the effect of tides, when the ratio of the orbital semi-major axes is
small and the mutual inclination is relatively large (greater than 20 degrees).
Using the quadrupolar non-restricted approximation for the gravitational
interactions and the viscous linear model for tides, we derive the averaged
equations of motion in a vectorial formalism which is suitable to model the
long-term evolution of a large variety of exoplanetary systems in very
eccentric and inclined orbits. In particular, it can be used to derive
constraints for stellar spin-orbit misalignment, capture in Cassini states,
tidal-Kozai migration, or damping of the mutual inclination. Because our model
is valid for the non-restricted problem, it can be used to study systems of
identical mass or for the outer restricted problem, such as the evolution of a
planet around a binary of stars. Here, we apply our model to three distinct
situations: 1) the HD80606 planetary system, for which we obtain the
probability density function distribution for the misalignment angle, with two
pronounced peaks of higher probability around 53 and 109 degrees; 2) the
HD98800 binary system, for which we show that initial prograde orbits inside
the observed disc may become retrograde and vice-versa, only because of tidal
migration within the binary stars; 3) the HD11964 planetary system, for which
we show that tidal dissipation combined with gravitational perturbations may
lead to a decrease in the mutual inclination, and a fast circularization of the
inner orbit.
