Ordered states of cellular flames, consisting of concentric rings of approximately equally sized cells, are observed over a wide range of parameters in our experiments using heavy hydrocarbon-air mixtures on a circular porous plug burner at low pressure. These ordered states have been found with cell numbers ranging from five to thirty. At a critical value of the flow rate, which depends on the equivalence ratio, a transition to a disordered state is observed, in which the ring structure disappears; the cells change their shape, size and number; and they move about in an irregular manner.