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 steady-state solutions intersect in the bifurcation diagram of for example, the degree of surface coverage of one of the adsorbates vs. 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 if 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.