In this paper, some new results of the study on the bistability and the instability of semiconductor optical amplifier are presented, which may be expected to be available to a class of excitonic optical bistable and amplifying systems. For these systems, both saturation and increasing absorptive bistability will product, depending on the competition among the interactions in the medium, especially the nonlinear couplings, and the lasing conditions. Particularly, the output curve appears a novel feature of optical hysteresis, with amplifying effect as well. On the other hand, the instability of the stationary states is investigated by linear stability analyzing. Some new phenomena of 'critical slowing down' are discovered near the relevant critical points, in the dynamic responding course.