The paper examined the steady-state multiplicity behaviour of the heterogeneous axial dispersion packed-bed reactor. Both intraparticle and interphase gradients of concentration and temperature are included in the mathematical model. An irreversible first-order reaction in the adiabatic and the nonisothermal-non-adiabatic regimes is considered. The method of orthogonal collocation is used to discretize the boundary value problem. The key parameter of the investigation is the reaction parameter (Thiele modulus). The effect of the other governing parameters is investigated.