A model for hydrostatic, fully nonlinear, low-mode internal tides is extended to continuously stratified conditions. Periodic inertia-gravity solutions of permanent form are shown to exist only for a limited range of amplitudes for a given stratification and frequency. As found in an earlier two-layer model, the solutions fall into two classes. In one, the waves take on a corner-shape as the limiting amplitude is approached. In the other, the waves remain continuous at the limiting amplitude, but have a lobate shape. Numerical investigation using the Euler equations shows that both classes of nonlinear solutions are robust to weak nonhydrostatic effects representative of oceanic conditions. The numerical solutions are also used to explore the evolution of an initial sinusoidal internal tide. It is demonstrated that the presence of the nonlinear solutions may limit the disintegration of the initial tide into shorter solitary-like waves. The nonlinear tide solutions and the disintegration process are briefly explored for conditions of the northeastern South China Sea where large internal tides and solitary waves are observed.