A tubular nonisothermal-nonadiabatic chemical reactor with consecutive reactions described by a set of three nonlinear parabolic equations, shows a sequence of period doubling bifurcations of a limit cycle. A numerical examination of the model reveals that complex periodic and irregular oscillations are possible. With increasing values of the Peclet number, regular and irregular oscillations are suppressed and disappear. The results of this numerical study may be used to explain turbulization of laminar flames.