A reverse saturable absorber is basically a classical saturable absorber ex
hibiting excited-state absorption. We investigate in this paper the dynamic
s of a laser with a reverse saturable absorber. A rate equation formalism i
s used to theoretically describe this laser. We first demonstrate, from a l
inear stability analysis, that excited-state absorption stabilizes the outp
ut intensity of a laser with a saturable absorber. Furthermore, the transie
nt dynamics are considered. We show that, depending on the characteristic t
ime associated with the reverse saturable absorber, the transient regime ca
n depart considerably from the classical relaxation oscillations usually ob
served in single-mode class-B lasers. We observe in some cases a large redu
ction of the first peaks of the relaxation oscillations.