We carry out a detailed orbit analysis of gravitational potentials selected at different times from an evolving self-consistent model galaxy consisting of a two-component disk (stars+gas) and a live halo. The results are compared with a pure stellar model, subject to nearly identical initial conditions, which are chosen as to make the models develop a large scale stellar bar. The bars are also subject to hose-pipe (buckling) instability which modifies the vertical structure of the disk. The diverging morphological evolution of both models is explained in terms of gas radial inflow, the resulting change in the gravitational potential at smaller radii, and the subsequent modification of the main families of orbits, both in and out of the disk plane. We find that dynamical instabilities become milder in the presence of the gas component, and that the stability of planar and 3D stellar orbits is strongly affected by the related changes in the potential -- both are destabilized with the gas accumulation at the center. This is reflected in the overall lower amplitude of the bar mode and in the substantial weakening of the bar, which appears to be a gradual process. The vertical buckling of the bar is much less pronounced and the characteristic peanut shape of the galactic bulge almost disappears when there is a substantial gas inflow towards the center. Milder instability results in a smaller bulge whose basic parameters are in agreement with observations. We also find that the overall evolution in the model with a gas component is accelerated due to the larger central mass concentration and resulting decrease in the characteristic dynamical time.
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