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

Evolution of eccentricity and orbital inclination of migrating planets in 2:1 mean motion resonance