A two-phase model for the non-isothermal fluidized-bed catalytic reactor with consecutive exothermic reactions has been used to investigate the bifurcation, instability and chaotic characteristics of this unit. The investigation, although in a restricted region of the parameters space, has uncovered a good part of the rich dynamic characteristics of this system, including 2" and 2"k period-doubling sequences leading to chaos, banded and fully developed chaos, interior crises, tangent bifurcation leading to intermittency, periodic windows interrupting chaotic regions and alternating periodic-chaotic sequences. Within the chaotic region a new type of periodic windows (termed periodic horns) which differ quantitatively and qualitatively from ordinary periodic windows has been discovered. Lyapunov exponents are also computed for the chaotic attractors in order to prove that they are truly chaotic and not strange non-chaotic attractors.