  First-order irreversible phase transitions (IPT's) between an active regime
and an absorbing state are studied in two models by means of both simulations
and mean-field stability analysis. Hysteresis around coexistence is the result
of the interplay of the length of the interface, its curvature, and a memory
effect related to the phase which is being removed. A controversy on the
occurrence of scale-invariance is clarified, conciliating the behavior of IPT's
with its reversible counterpart.
