  In this paper, we present a formalism designed to model tidal interaction
with a viscoelastic body made of Maxwell material. Our approach remains regular
for any spin rate and orientation, and for any orbital configuration including
high eccentricities and close encounters. The method is to integrate
simultaneously the rotation and the position of the planet as well as its
deformation. We provide the equations of motion both in the body frame and in
the inertial frame. With this study, we generalize preexisting models to the
spatial case and to arbitrary multipole orders using a formalism taken from
quantum theory. We also provide the vectorial expression of the secular tidal
torque expanded in Fourier series. Applying this model to close-in exoplanets,
we observe that if the relaxation time is longer than the revolution period,
the phase space of the system is characterized by the presence of several
spin-orbit resonances, even in the circular case. As the system evolves, the
planet spin can visit different spin-orbit configurations. The obliquity is
decreasing along most of these resonances, but we observe a case where the
planet tilt is instead growing. These conclusions derived from the secular
torque are successfully tested with numerical integrations of the instantaneous
equations of motion on HD 80606b. Our formalism is also well adapted to
close-in super-Earths in multiplanet systems which are known to have non-zero
mutual inclinations.
