  To date, more than 100 giant Jupiter-like planets have been discovered in
Doppler surveys of solar-type stars. In this paper, we perform simulations to
investigate three systems: GJ 876, HD 82943 and 55 Cnc. The former two systems
both have a pair of planets in the 2:1 Mean Motion Resonance (MMR), while the
inner two companions of the later is close to 3:1 MMR. By integrating hundreds
of the planetary orbits of three systems for million years, we find that for GJ
876 and HD 82943, the critical argument $\lambda_{1} - 2\lambda_{2} +
\varpi_{1}$ and $\lambda_{1} - 2\lambda_{2} + \varpi_{2}$ librate about
$0^{\circ}$ or $180^{\circ}$, indicating 2:1 MMR can play an important role in
stabilizing the motion of the planets so that they are protected from frequent
close encounters. As for 55 Cnc, we further show the three resonant arguments
for 3:1 MMR execute librations for millions of years respectively, which
reveals the evidence of the resonance for this system. Additionally, we should
emphasize another vital mechanism is the apsidal phase-locking between a couple
of planets for a certain system. For GJ 876 and HD 82943, we discover the
relative apsidal longitudes $\varpi_{1} - \varpi_{2}$ move about $0^{\circ}$ or
$180^{\circ}$, respectively; but for 55 Cnc, we find that there exists an
asymmetric apsidal libration between two inner planets. Finally, we made a
brief discussion about the Habitable Zones in the exoplanetary systems.
