  We determine, analytically and numerically, the conditions needed for a
system of two migrating planets trapped in a 2:1 mean motion resonance to enter
an inclination-type resonance. We provide an expression for the asymptotic
equilibrium value that the eccentricity $e_{\rm i}$ of the inner planet reaches
under the combined effects of migration and eccentricity damping. We also show
that, for a ratio $q$ of inner to outer masses below unity, $e_{\rm i}$ has to
pass through a value $e_{\rm i,res}$ of order 0.3 for the system to enter an
inclination-type resonance. Numerically, we confirm that such a resonance may
also be excited at another, larger, value $e_{\rm i, res} \simeq 0.6$, as found
by previous authors. A necessary condition for onset of an inclination-type
resonance is that the asymptotic equilibrium value of $e_{\rm i}$ is larger
than $e_{\rm i,res}$. We find that, for $q \le 1$, the system cannot enter an
inclination-type resonance if the ratio of eccentricity to semimajor axis
damping timescales $t_e/t_a$ is smaller than 0.2. This result still holds if
only the eccentricity of the outer planet is damped and $q \lesssim 1$. As the
disc/planet interaction is characterized by $t_e/t_a \sim 10^{-2}$, we conclude
that excitation of inclination through the type of resonance described here is
very unlikely to happen in a system of two planets migrating in a disc.
