The spectra of pressure oscillations in combustion chambers often contain large peaks at frequencies corresponding to chamber acoustic modes. Pulsed combustors are designed to operate with fixed amplitude oscillations but in many systems the oscillations have undesirable consequences. An understanding of the nonlinear mechanisms responsible for the limiting-amplitude behavior is therefore desired. This paper is divided into two parts. First, characterization of the oscillations in terms of attractors in mathematical phase space has been performed on pressure signals measured in a laboratory combustor of premixed gases. The results for one set of operating conditions show a quasiperiodic attractor of dimension two over an order of magnitude of scales. Next, the nonlinear combustion response to oscillations of a single acoustic mode are used to model autonomous or 'self-excited' behavior. Tho simple models of nonlinear combustion processes observed in the laboratory combustor result in unstable oscillations that reach limiting-amplitudes. With the variation of model parameters. the periodic limit cycles undergo subharrnonic bifurcations and transition to chaos.