A method is developed to determine parameters of a reactor model, which explicitly define a set of states in an adiabatic tubular fixed-bed reactor with vanishing propagation velocity of the thermal front. The vanishing front propagation velocity constitutes the definition of a steady state in the reactor from the point of view of the dynamics of the process. Therefore the knowledge of the parameters mentioned above is crucial for a general characteristics of the propagation process of the thermal front in the reactor. It is found that the position of the temperature and conversion profiles in the reactor is uniquely determined by the value of a single parameter chosen (e.g., the feed temperature or the mixture flow rate in the reactor). The variation in this parameter leads to the propagation of the reaction front until a different steady state is established or the reactor is extinguished altogether. A simultaneous bifurcation analysis reveals that, over the multiplicity region, only three steady states can exist of which two are stable and one is unstable. Consequently, all steady states associated with high conversion degrees (y similar to 1) and vanishing front propagation velocity, independently of their position within the reactor, from the standpoint of bifurcation analysis represent steady states located on the upper stable branch of the bifurcation diagram. No reasons thus exist to differentiate between these states. An approximate method is proposed for evaluating the range of inlet temperatures over which steady states with zero propagation velocity appear in the reactor.