Processes which reduce IO3- to I-2 and O-2 and which oxidize I-2 to IO3- in an aqueous, moderately acidic medium may alternate in dominance during iodate ion catalysis of the disproportionation of H2O2 to H2O and O-2. We have used a skeleton mechanism proposed previously to develop a model of this system based on only two concentration variables, [I-2] and [O-2], and three composition parameters. The properties of this model ate explored both analytically and numerically. Numerical integration for certain parameter values shows oscillation of [O-2] and [I-2] around an unstable steady state. However, while these oscillations can be quite long-lived they take place around a stable or unstable focus and do not involve a true limit cycle. The changes of parameter values which cause the steady state to be stable or oscillatory are consistent with the experimental effects of changing acidity or stirring rate. Although the behavior of our mathematical model is remarkably consistent with our experimental observations, we can not claim to have developed a complete elucidation of the mechanism of the overall reaction.