Several studies on membrane reactors for hydrogen production have shown that the permeation of hydrogen may be inhibited by the competitive adsorption of one or more of the reactants. This adsorption-inhibition effect, often accounted for in rate expressions of catalytic reactions, may induce the existence of multiple steady state solutions. In this work we investigate the possible presence of bistability in membrane reactors. We start with the study of a mixed membrane reactor, which allows for the analytical derivation of a bistability criterion, and then extend the analysis, numerically, to a fixed bed membrane reactor. Under conditions of an infinitely fast reaction, the bifurcation parameters are dimensionless versions of the equilibrium constant of the reaction, the membrane permeability, and the adsorption constant of the inhibiting reactant. In the Conclusions we discuss the design implications, and assess whether this phenomenon can be realized in practice.