The nonlinear dynamics of a solid-state ring laser (SSRL) is studied t
heoretically and experimentally. We have identified the parametric mec
hanism for the excitation of the relaxation oscillations in an autonom
ous SSRL operating in the self-modulation regime of the first kind. Th
e nonlinear shifts of the frequencies of the relaxation and self-modul
ation oscillations and their mutual synchronization in zones of parame
tric resonance are investigated. It is shown that in these regions the
following bifurcations can occur: doubling of a period of the self-mo
dulation oscillations and the appearance of dynamical chaos. The spect
rum oi the Lyapunov exponents and the information dimension of the str
ange attractor have been found. It is shown that using a semiclassical
model of SSRL one can explain all experimentally observed features of
the nonlinear dynamics of the ring laser under consideration.