A reverse saturable absorber is basically a classical saturable absorber exhibiting excited-state absorption. We investigate in this paper the dynamics of a laser with a reverse saturable absorber. A rate equation formalism is used to theoretically describe this laser. We first demonstrate, from a linear stability analysis, that excited-state absorption stabilizes the output intensity of a laser with a saturable absorber. Furthermore, the transient dynamics are considered. We show that, depending on the characteristic time associated with the reverse saturable absorber, the transient regime can depart considerably from the classical relaxation oscillations usually observed in single-mode class-B lasers. We observe in some cases a large reduction of the first peaks of the relaxation oscillations.