We explain numerical results on a periodically perturbed Oregonator by Markman and Bar-Eli (J. Phys. Chem. 98 12248 (1994)). If the dynamics of the system is governed by a family of diffeomorphisms of a circle with a Devil's staircase one will expect the observed behavior, i.e. (1) Only periodic solutions are found in frequency-locked steps, each with some pattern of large and small oscillations (2) Between any two speps there is a step with the period being the sum of the periods and the concatenated pattern (3) Scaling as the period tends to infinity. Using invariant manifold theory we argue that an invariant circle must indeed exist when, as in the case under consideration, the unperturbed system is close to a saddle-node bifurcation on a limit cycle. Generalisations of the results are discussed.