The interaction between self-modulation and relaxation oscillations in
a solid-state ring laser operating in a self-modulation regime of the
first kind is investigated theoretically. It is shown that the region
s of parametric resonances between the self-modulation and relaxation
oscillations have a strong influence on the stability of the former os
cillations. The limits of the parametric instability bands and growth
increments of the relaxation oscillations are found.