The steady-state multiplicity features of an adiabatic fixed bed reactor were Investigated experimentally by the methanation of either CO or CO2 as test reactions. No more than two stable steady states were found at any operating conditions. The Langmuir-Hinshelwood kinetics of these reactions caused the conversion along the lower branch to decrease with increasing feed concentration. The experimental results have been explained and simulated by a one-dimensional two-phase model which accounts for axial dispersion as well as inter- and intraphase transport resistances. The surface describing the conversion as a function of feed concentration and temperature has the shape of a cusp for CO2 methanation and of a pitchfork for CO methanation.