Observatorio Astronmico "Felix Aguilar", Universidad Nacional de San Juan, Argentina.
We have studied the dynamical behavior of asteroids in resonance with Jupiter using numerical methods over 10(6) - 10(7) yr. The aim of this paper is to discuss some numerical results obtained from the integration of orbits computed for a long time span. We have analyzed the behavior of the elliptical elements and their variation with time for obtaining dynamics information (collision or escape). We have compared these results with the Lyapunov times obtained for each orbit. Also, we have studied the topology of phase space by constructing the surfaces of section. We present the results obtained for the 2:1 and 3:2 resonances.