  The motion of two planets around a Sun-like star under the combined effects
of mutual interaction and tidal dissipation is investigated. The secular
behaviour of the system is analyzed using two different approaches. First, we
solve the exact equations of motion through the numerical simulation of the
system evolution. In addition to the orbital decay and circularization, we show
that the final configuration of the system is affected by the shrink of the
inner orbit. Our second approach consist in the analysis of the stationary
solutions of mean equations of motion based on a Hamiltonian formalism. We
consider the case of a hot super-Earth planet with a more massive outer
companion. As a real example, the CoRoT-7 system is analyzed solving the exact
and mean equations of motion. The star-planet tidal interaction produces
orbital decay and circularization of the orbit of CoRoT-7b. In addition, the
long-term tidal evolution is such that the eccentricity of CoRoT-7c is also
circularized and a pair of final circular orbits is obtained. A curve in the
space of eccentricities can be constructed through the computation of
stationary solutions of mean equations including dissipation. The application
to CoRoT-7 system shows that the stationary curve agrees with the result of
numerical simulations of exact equations. A similar investigation performed in
a super-Earth-Jupiter two-planet system shows that the doubly circular state is
accelerated when there is a significant orbital migration of the inner planet,
in comparison with previous results were migration is neglected.
