  Pairs of planets in a system may end up close to their host star on eccentric
orbits as a consequence of planet planet scattering, Kozai or secular
migration. In this scenario, general relativity and secular perturbations have
comparable timescales and may interfere with each other with relevant effects
on the eccentricity and pericenter evolution of the two planets. We explore,
both analytically and via numerical integration, how the secular evolution is
changed by general relativity for a wide range of different initial conditions.
We find that when the faster secular frequency approaches the general
relativity precession rate, which tipically occurs when the outer planet moves
away from the inner one, it relaxes to it and a significant damping of the
proper eccentricity of the inner planet occurs. The proper eccentricity of the
outer planet is reduced as well due to the changes in the secular interaction
of the bodies. The lowering of the peak eccentricities of the two planets
during their secular evolution has important implications on their stability. A
significant number of two planet systems, otherwise chaotic because of the
mutual secular perturbations, are found stable when general relativity is
included.
