  We investigate the inclination-growth mechanisms for two-planet systems
during the late protoplanetary disc phase. In previous works, much attention
has been directed to the inclination-type resonance, and it has been shown that
it asks for high eccentricities to be acquired during the migration of the
giant planets. By adopting eccentricity and inclination damping formulae based
on hydrodynamical simulations (instead of the K-prescription), we have carried
out 20 000 numerical simulations, where we vary the initial planetary
eccentricities, the migration rate, and the dispersal time of the gas disc. Our
results confirm that highly mutually inclined systems are unlikely to be
produced by an inclination-type resonance of two migrating giant planets.
However, in ~1 per cent of the simulations, inclination-type resonance is
observed, and a dynamical study of the evolutions reveals that the
inclination-type resonance mechanism operates in three cases: (i) when the
inner planet reaches the inner cavity of the disc, (ii) at moderate to high
eccentricities for faster migration rates, and (iii) at low to moderate
eccentricities after a phase of orbital destabilization and re-arrangement.
