The long-term stability of the evolution of two-planet systems is considered by using the general three body problem ( GTBP ) . Our study is focused on the stability of systems with adjacent orbits when at least one of them is highly eccentric . In these cases , in order for close encounters , which destabilize the planetary systems , to be avoided , phase protection mechanisms should be considered . Additionally , since the GTBP is a non-integrable system , chaos may also cause the destabilization of the system after a long time interval . By computing dynamical maps , based on Fast Lyapunov Indicator , we reveal regions in phase space with stable orbits even for very high eccentricities ( e > 0.5 ) . Such regions are present in mean motion resonances ( MMR ) . We can determine the position of the exact MMR through the computation of families of periodic orbits in a rotating frame . Elliptic periodic orbits are associated with the presence of apsidal corotation resonances ( ACR ) . When such solutions are stable , they are associated with neighbouring domains of initial conditions that provide long-term stability . We apply our methodology so that the evolution of planetary systems of highly eccentric orbits is assigned to the existence of such stable domains . Particularly , we study the orbital evolution of the extrasolar systems HD 82943 , HD 3651 , HD 7449 , HD 89744 and HD 102272 and discuss the consistency between the orbital elements provided by the observations and the dynamical stability .