A model and computation for oscillatory phenomena observed in some biological processes that utilize ion gradients across a membrane is presented. The model contains two main features: (i) active H+ transport pathways in the membrane and (ii) key enzymes having a pH-dependent activity profile and either translocating H+ from outside or producing H+ as a product. With this model a very long period of oscillations, as observed in mitochondrial and circadian rhythms, could be quantitatively demonstrated.