A type of sustained oscillations that can occur in the output of semiconductor injection lasers are studied analytically. The frequency of oscillations and the conditions of instability are deduced from the nonlinear differential rate equations. This model raises the possibility that, at least in some if not many cases, the stability of a laser above threshold is determined by the degree of saturation of the optical gain. If the gain saturates, the laser is stable, and disturbances become damped oscillations. If the gain increases above the standard value, there will be some current level above threshold at which oscillations become sustained. Furthermore, the condition for critically damping the transient ringing in laser output is also derived analytically. The results of the analysis are compared with the limited experimental results available and the agreement is reasonable. The analysis also provides general guidelines for the design of injection lasers that will be less susceptible to instabilities in their optical output.