The nonlinear behavior ot acoustic rays in underwater sound channels is examined using a set of parabolic ray equations. Two sound speed profiles, a Munk canonical and a double-duct profile, are investigated. For range-independent but stratified ocean sound speed profiles, analytical results concerning the sound ray trajectory and wave length are obtained. The stability of the system is found to be marginal stable, which leads to the phenomenon of wave front folding. Next, a perturbed system attributed to a single-mode internal wave is examined. The stability, bifurcation and other nonlinear dynamic issues of the nearly integrable system are explored using a combination of phase plane trajectories, Poincaré maps, bifurcation diagrams, Lyapunov exponents and Floquet multipliers.