Dynamics of both classical and semiclassical models of single-mode solid-state lasers with different Q-spoilers is investigated within bifurcation of the cycle creation approach. Stability criteria of the periodical oscillation of the intensity, which are appear due to the Hopf bifurcation, and stability intervals for the models parameters are studied. Bifurcation processes within semiclassical model of the single-mode running wave lasers are analyzed. Both three and four-dimensional laser models are integrated within the Josephs method.