Theory is presented for the rotation speed dependence of the transport-limited current at a rotating-disc electrode for the case where the substrate reacts via a CE mechanism. The theoretical approach adopted solves the relevant coupled mass-transport equations by means of an explicit finite-difference method employing a non-linear spatial coordinate (obtained by ‘Hale transformation’) which covers the diffusion layer at the electrode. The approach is generalised to the case where the participating species have arbitrary and unequal diffusion coefficients. This allows us to provide ‘working curves’ for the analysis of CE processes, measured under steady-state conditions at rotating disc electrodes, which make no assumptions as to the magnitude of the rate constant of the chemical step or about the equality(or otherwise) of the diffusion coefficients of the species involved in the reaction. This represents a significant advance on previous work on this problem. The corresponding theoretical descriptions relating to the chronoamperometric response arising from a potential step at the electrode are also presented.