The oscillations of the Belousov-Zhabotinskii reaction in a batch reac
tor vanish due to the consumption of the main reactants, i.e. bromate
and malonic acid. This behavior has been analyzed first using the clas
sical Oregonator model, where reactant concentrations are kept constan
t, and then introducing a modified model, in which the reactant concen
tration is allowed to vary according to the stoichiometry of the consi
dered set of chemical reactions. Two different routes to the extinctio
n of oscillations have been found, depending on whether the Oregonator
exhibits a subcritical or a supercritical Hopf bifurcation. These the
oretical findings are consistent with the experimental observations, t
hat indicate that the disappearance of the oscillations takes place in
two rather different ways: either suddenly after a series of practica
lly undamped oscillations or through very slowly damped oscillations.