Orbits for 615 halo and high-velocity disk stars have been numerically integrated in two different models for the galactic mass distribution, both satisfying recent observational constraints for the rotation curve and the perpendicular force (Allen and Martos 1986, Allen and Santillán 1991). In spite of major differences in the mathematical form of both models for the galactic potential, the orbital parameters of most of the computed orbits do not change appreciably. The greatest differences are found in the apogalactic distances reached by weakly bound stars, in the heights above galactic plane, and most importantly, in the total fraction of chaotic as opposed to semiperiodic orbits found for each galactic potential model.