A number of nonmonotonic behaviors appear when the Belousov–Zhabotinsky reaction is run in a flow system (CSTR) which are not observed when the reaction is run in a closed system. Among these behaviors is composite double oscillation in which nearly identical bursts of oscillation are separated by regular periods of quiescence. Here we use a modified version of the oregonator model of the Belousov–Zhabotinsky reaction to simulate composite double oscillation. Our modification involves the addition of a new variable which is related to the amount of brominated organic material present in the system. This new variable changes slowly on the time scale of the oscillations and controls the value of f, the stoichiometric factor of step 5 in the oregonator. Thus the behavior of the modified oregonator in CSTR mode when flowrates are moderate can be rationalized in terms of the properties of the unmodified oregonator in a closed system. We show that composite double oscillation is a hysteresis phenomenon occurring over a small range of values of f where a locally stable steady state and a locally stable limit cycle coexist. Composite double oscillation occurs as the system is carried back-and-forth across the area of coexistence by the new, slowly moving variable whose concentration grows during the oscillatory phase, when the system is on the locally stable limit cycle, and decays during the quiescent phase, when the system is on the locally stable steady state.