A two-phase model for the non-isothermal fluidized bed catalytic reactor with consecutive exothermic reactions used earlier to investigate the chaotic behaviour of this system(1) is used in this investigation to explore the behaviour in a different region of parameters to demonstrate the existence of complex non-chaotic behaviour. It is found that relaxation oscillations develop through distortion of Limit cycles which have fast and slow motion in the different region of the phase space. A new type of period-adding bifurcation of the Poincare’ return points is uncovered and is shown to generate periodic bursting with a complex ’strange’ geometrical structure. The period-adding mechanism presented is classified as a third kind of period-adding according to the classification of Holden and Fan(27). It is conjecture that the complex oscillatory trajectory is terminated by a boundary crisis.