  We carry out numerical simulations to explore the dynamical evolution of the
HD 82943 and HD 37124 planetary systems,which both have two Jupiter-like
planets. By simulating various planetary configurations in the neighborhood of
the fitting orbits, we find three mechanisms to maintain the stability of these
systems: For HD 82943,we find that the 2:1 mean motion resonance can act as the
first mechanism for all the stable orbits. The second mechanism is the
alignment of the periastron of the two planets of HD 82943 system. In the
paper,we show one case is simultaneously maintained by the two mechanisms.
Additionally,we also use the corresponding analytical models successfully to
explain the different numerical results for the system. The third mechanism is
the Kozai resonance which takes place in the mutual highly orbits of HD 37124.
In the simulations,we discover that the argument of periastron $\omega$ of the
inner planet librates about $90^{\circ}$ or $270^{\circ}$ for the whole time
span. The Kozai mechanism can explain the stable configuration of large
eccentricity of the inner planet.
