Singularity theory is combined with the continuation technique to classify the steady-state and dynamic behavior of a well-mixed two-phase (catalytic) adiabatic reactor model. Due to the presence of boundary limit sets (corresponding to ignition or extinction of the particles at zero residence time) and boundary Hopf sets (corresponding to oscillatory behavior of the catalyst particles), the steady-state and dynamic behavior of the heterogeneous model is found to be profoundly different from that of the pseudohomogeneous model. It is observed that the values of the particle Lewis number, Le(p) (ratio of interphase heat to mass transfer coefficients), and the particle Damkohler number, Da(p), determine the regions where the pseudohomogeneous model predictions break down. For Le(p) greater than or equal to 1, the maximum temperature in both the solid and fluid phases is the adiabatic temperature rise. However, for Le(p) < 1, it is shown that the particles can ignite (at zero residence time) and the temperature in the solid phase can be as high as B/Le(p), where B is the adiabatic temperature rise. The maximum temperature in the fluid phase is always less than the adiabatic temperature rise. In addition, it is found that isolated high temperature branches can exist in the adiabatic reactor when Le(p) < 1. From the dynamic classification, it is observed that, for Le(p) > 1, both high- and low-temperature oscillations are likely to occur for practical values of the parameters.