We study superconducting YBaCuO microwave resonators, with an integrated microbridge, and their response to a monochromatic injected signal. In a bound region in the input power-input frequency plane, and close to a resonance frequency ω₀, a nonlinear phenomenon of self-sustained modulation of the reflected power off the resonator is observe. We attribute this behavior to thermal instability in the microbridge, which alternately oscillates between normal- and super-conductive phases, and shifts ω₀ back and forth. Additional non-linear behavior of the reflected signal, such as period doubling bifurcation and jumping between different self-modulation frequencies, is also demonstrated, and is attributed to coupling of several closely lying resonance frequencies in the resonator. We generalize a theoretical model which we previously presented, to a multimode case. The generalized model can account for the various phenomena in the experimental data, both in the case of single mode self-modulation, and in the case where coupling between several modes is involved.