- Gas-kinetic theory and N-body simulations are used to determine the stability of the self-gravitating and nonuniformly rotating particulate Saturnian ring disk against small-amplitude gravity perturbations. It is showin that as a result of the classical Jeans-type instability of gravity disturbances (e.g., those produced by a spontaneous perturbation and/or a companion system) the disk is subdivided into numerous irregular ringlets, with size and radial spacing between them of the order of 2 pi h ˜ 100 m or even less, where h is the local thickness of the system. We predict that Cassini spacecraft high-resolution images may reveal this kind of tightly-wound spiral structure in the main rings A, B, and C of the Saturnian ring system. Acknowledgement. This work was supported in part by the Israel Science Foundation and the Israeli Ministry of Immigrant Absorption.