We investigate the influence of a finite absorber relaxation time on passively mode-locked semiconductor lasers. We find that the mode-locking mechanism of Haus is surprisingly susceptible to small perturbations and small changes in the parameters. Even when the absorber relaxation time is much larger than the pulse duration, it typically is still short enough to be a crucial part of the physics of mode-locking. Allowing for a finite absorber relaxation time, we find that stable operation of a mode-locked semiconductor is possible over a wide range of parameters. We argue that the pulse duration is inversely proportional to the square root of the pulse energy. ©1997 American Institute of Physics.