A quantitative analysis of the autothermicity and multiplicity of steady states for methanol synthesis in a fluidized-bed reactor cooperating with an external heat exchanger has been performed. As it was shown previously [1], methanol synthesis can be carried out in a single fluidized-bed reactor. However; to obtain technologically acceptable yields, the substrates should be preheated to a relatively high temperatures which increases the operational costs. It was shown [2] that there are available autothermal configurations which help us to overcome this problem. One of such solutions is based in the installation of an external autothermal heat exchanger in which the substrates are preheated. It is characterized by internal heat feedback resulting from the fluidized-bed structure as well as by external heat feedback resulting from the presence of the autothermal heat exchanger. Similarly as in [1], the fluidized-bed reactor was described by a three-phase multi-compartment model. Such a model comprises of a set of nonlinear algebraic or transcendental equations. In the case of nonisothermal processes each compartment is described by a set of 3(N + 1) equations where N is the number of linearly independent chemical reactions. In our case N = 2. In order to obtain the solution of the model equations two determining functions are defined: the first one results from the heat balance of the emulsion phase, the second - from the heat balance of the exchanger. The kinetics of the methanol synthesis was described by the equations proposed by TAKAGAWA and OHSUGI [5]. In order to obtain the results enabling evaluation of the effects of the installation of the autothermal heat exchanger, a series of numerical computations was performed. The aim of these computations was to determine the hysteresis loops and the catastrophe sets. At the first stage the influence of the pressure under which the process has been carried out and the heat exchanger size were determined. For sufficiently low pressures only unique steady states exist similarly as for sufficiently small heat exchangers independently of the pressure. An interesting result is shown in figure 2. The region of heat exchanger sizes exists where with gradual increase of the pressure, the system twice crosses the catastrophe set. The cross section of the catastrophe set with the plane (A(q)k(q)/S,p) consists of two branches of singularity codimension one of which meets at a point of singularity codimension two. In Figure 3 the influence of the feed temperature is shown. The installation of a sufficiently large heat exchanger allows one to use feed of lower temperature, remaining on the higher steady states. Furthermore, in Fig. 3 the cross section of the catastrophe set is shown. In Figure 4 a few representative histeresis loops and the cross section of the catastrophe set on the plane (A(q),k(q)/S,u(o)/u(mf)) are shown. As we can see, the catastrophe set divides the plane into two regions where unique and multiple steady states can be realized. The influence of the deformation of the external feedback is shown in Fig. 5 where a few representative bifurcation curves and the catastrophe set are displayed. The main practical consequence of the installation of an autothermal heat exchanger is the possibility of decreasing the feed temperature and the process pressure still remaining in the higher steady state region. These results are in agreement with the general theory of the autothermal systems.