  The formation of resonant pairs of planets in exoplanetary systems involves
planetary migration in the protoplanetary disc. After a resonant capture, the
subsequent migration in this configuration leads to a large increase of
planetary eccentricities if no damping mechanism is applied. This has led to
the conclusion that the migration of resonant planetary systems cannot occur
over large radial distances and has to be terminated sufficiently rapidly
through disc dissipation.
  In this study, we investigate whether the presence of an inner disc might
supply an eccentricity damping of the inner planet, and if this effect could
explain the observed eccentricities in some systems. To investigate the
influence of an inner disc, we first compute hydrodynamic simulations of giant
planets orbiting with a given eccentricity around an inner gas disc, and
measure the effect of the latter on the planetary orbital parameters. We then
perform detailed long term calculations of the GJ 876 system. We also run
N-body simulations with artificial forces on the planets mimicking the effects
of the inner and outer discs.
  We find that the influence of the inner disc can not be neglected, and that
it might be responsible for the observed eccentricities. In particular, we
reproduce quite well the orbital parameters of a few systems engaged in 2:1
mean motion resonances: GJ 876, HD 73526, HD 82943 and HD 128311. Finally, we
derive analytically the effect that the inner disc should have on the inner
planet to reach a specific orbital configuration with a given damping effect of
the outer disc on the outer planet.
