The assumption of irreversible adsorption of a reactant can lead to a structurally unstable kinetic model. The structural instability is caused by the fact that two steadystate solutions intersect in the bifurcation diagram o j for example, the degree of surface coverage of one of the adsorbates us. the partial pressure of one of the reactants. One of the two solutions is a trivial solution, corresponding to a catalyst surface completely covered with the irreversibly adsorbing reactant. The intersection point is a transcritical bifurcation point. A structurally stable kinetic model is obtained i f an arbitrarily small desorption rate coefficient is introduced. Two examples are discussed in which a transcritical bifurcation point is encountered, that is, the total oxidation of ethene in three-way catalysis and the chemical vapor deposition of refractory metals. The consequences of the existence of a transcritical bifurcation point for kinetic parameter estimation and reactor simulation are emphasized.