A four-variable CSTR model proposed by Rabai and Orban to describe a number of chlorite-containing oscillatory reactions produces complex periodic oscillations and chaos. Detailed numerical simulations and two-parameter bifurcation diagrams with changing inflow concentrations and rate constants were calculated to reveal the dynamical properties of the model and to compare them with the results of experiments on systems containing chlorite- and sulfur-containing reductants such as thiosulfate, thiocyanate, and thiourea. It is suggested that the model requires more flexibility in describing the variable stoichiometry of the sulfur-containing reductants and that it may need to account for the reactivity of chlorine dioxide. Experiments are suggested to establish the values of some of the parameters and to illuminate mechanistic uncertainties in the model.