Kinetic theory with the Boltzmann and Poisson's equations is used to determine the stability and oscillations of the two-dimensional collisional system of identical particles of Saturn's rings. The effects of physical collisions between particles are taken into account by using in the Bolztmann kinetic equation a phenomenological Bhatnagar-Gross-Krook collisional integral (Bhatnagar et al. 1954). This model collisional integral was modified following Shu & Stewart (1985) to allow collisions to be inelastic. The dynamics of a system with rare collisions is considered, that is, Omega(2) much greater than nu(c)(2), with Omega being the orbital angular frequency and nu(c) the collision frequency. It is shown that in a Jeans-stable system the simultaneous action of self-gravity and collisions leads to a secular dissipative type instability. It is also shown that generally the growth rate of this aperiodic instability is small, Im omega* similar to nu(c). However, in the marginally Jeans-stable gravitationally parts of the disk, the growth rate is a maximum, and may become a large, Im omega* similar or equal to (nu(c) Omega(2))(1/3) much greater than nu(c). In such parts of the Saturn's system the instability will develop on the time scale only of several revolutions even at moderately low values of the local optical depth, tau similar or equal to nu(c)/Omega similar to 0.1. The radial wavelength of the most unstable oscillations is of the order lambda similar or equal to 2 pi rho, where rho similar or equal to c/Omega is the epicyclic radius and c is the mean dispersion of random velocities of particles. The secular instability may be suggested as the cause of much of the irregular, narrow similar to 2 pi rho similar to 100 m structure in low optical depth regions of Saturn's rings. Cassini spacecraft high-resolution images may resolve such hyperfine structure in the C ring, the inner B ring and the A ring.
