The study result shows that in open resonant lower-ladder and V systems, the destabilization of the nonlasing solution can occur through a Pitchfork bifurcation giving rise to continuous wave lasing without inversion (LWI), and also through a Hopf bifurcation giving rise to self-pulsing LWI. This paper also analyzes the effect of the unsaturated gain parameter, damping rate of cavity , ratio of the atomic injection rates and atomic exit rate on the two instabilities.