Instabilities and strong dynamical interactions between multiple giant planets have been proposed as a possible explanation for the surprising orbital properties of extrasolar planetary systems . In particular , dynamical instabilities seem to provide a natural mechanism for producing the highly eccentric orbits seen in many systems . Previously , we performed numerical integrations for the dynamical evolution of planetary systems containing two giant planets of equal masses initially in nearly circular orbits very close to the dynamical stability limit . We found the ratio of collisions to ejections in these simulations was greater than the ratio of circular orbits to eccentric orbits among the known extrasolar planets . Further , the mean eccentricity of the planets remaining after an ejection was larger than the mean eccentricity of the known extrasolar planets . Recently , we have performed additional integrations , generalizing to consider two planets of unequal masses . Our new simulations reveal that the two-planet scattering model can produce a distribution of eccentricities consistent with the observed eccentricity distribution for plausible mass distributions . Additionally , this model predicts a maximum eccentricity of about 0.8 , in agreement with observations . Early results from simulations of three equal-mass planets also reveal a reduced frequency of collisions and a broad range of final eccentricities for the retained inner planet .