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 _ { 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 _ { i } has to pass through a value e _ { 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 _ { 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 _ { i } is larger than e _ { i,res } .
We find that , for q \leq 1 , the system can not 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 .