The principles underlying electrochemical oscillators on mercury have been known for three decades. They are (1) the existence of a negative charge transfer resistance, (2) the general coupling between interfacial kinetics and mass transport, and (3) the inclusion of the effects of additional impedances, such as the double layer capacitance and any series (film, solution, and external) resistances. The charge transfer resistance needs to be defined in general rather than within the confines of a specific model, such as that of Erdey-Gruz and Volmer. The effects of the double layer capacitance and of series resistance can be incorporated by using general stability criteria for electrical circuits. The above effects suffice for a quantitative representation of several types of oscillations observed at the mercury \ water interface. Electrochemical oscillations are typically non-linear, and closed-form analytical solutions are not available. Models in which diffusion is approximated in terms of Nernst diffusion layers are useful for experiments enforcing stationary mass transport conditions, as with rotating disk electrodes, but do not apply to measurements on hanging or dropping mercury electrodes. Digital simulations do not require such steady-state approximations. (C) 2003 Elsevier Science B.V. All rights reserved.