It is now known that many spiral density waves in Saturn’s C ring are forced by resonant gravitational interactions with the planet’s nonradial oscillations. Observations of their periods have the power to reveal new information concerning subtle aspects of the planet’s internal structure. The properties of a certain class of nonradial oscillations, consisting of the inertial and rotational normal modes (i-modes and r-modes), are particularly sensitive to small departures of the internal density stratification from adiabatic, and may be especially useful in revealing such departures and their implications for any compositional gradients residing inside Saturn. We calculate the frequencies and eigenfunctions (shapes) of the i-modes and r-modes for a given suite of internal structure models and determine the Lindblad resonance locations and periods of the density waves they excite in the C ring. We find that for reasonable models of Saturn’s internal structure, the i-mode and r-mode frequencies overlap the range of frequencies of the slowest density waves observed in the C ring, that is, those having pattern speeds similar to Saturn’s rotation rate. In addition, the presence of observable density waves forced by r-modes requires Saturn to possess (at least) two statically stable (non-convective) regions, one in the deep interior and the other in the outer molecular hydrogen envelope. The inner zone is most likely stabilized by a significant compositional gradient, the outer zone by a compositional gradient, by baroclinic processes, or both. Unresolved questions remain. Currently, the model predicts that if energy is equipartitioned among the i-modes, then some slow density waves should be detectable at radii inside ~84500 km in the C ring. None have been observed inside this radius. In addition, the source of excitation of the normal modes remains to be identified. We are currently exploring whether they can draw their energy from baroclinic instability in the outer stable zone. These questions will be addressed at length at the meeting. This work is supported by the NASA SSW program.