The coexistence between two stable steady states, referred to as bistability, is generally associated with a phenomenon of hysteresis in which a system jumps back and forth between the two branches of stable states for different critical values of some control parameter, corresponding to two limit points. In a previous publication (Guidi, G.; Goldbeter, A. J. Phys. Chem. A 1997, 101, 9367) we focused on the cases where one of the limit points becomes inaccessible or goes to infinity. Under such conditions it becomes impossible to achieve the transitions between the two branches of stable steady states as a result of variation of a single parameter : bistability ceases to be associated with hysteresis. We referred to these two cases as irreversible transitions of type 1 or type 2, respectively. To study in detail the conditions under which such irreversible transitions between multiple steady states occur in chemical systems, two models based on fully reversible chemical steps were considered. The first model, due to Schlogl, was shown to admit irreversible transitions of type 1 as one of the limit points associated with bistability moves into a physically inaccessible region of negative values of a control parameter. A second, original model was proposed to illustrate the case of irreversible transitions of type 2 in which a limit point goes to infinity. Here, by fusing these two models, we construct a hybrid model to analyze the conditions in which irreversible transitions of types 1 and 2 both occur as a function of a given control parameter. Then bistability still exists, but the branches of coexisting steady states cease to be connected so that the transitions between the two stable steady states can no longer be achieved, regardless of the direction of variation in the control parameter. Such transitions might only result from a change in some other control parameter or from chemical perturbation.