A full mathematical description of impedance voltammetry and demodulation voltammetry is given for the case where the electrode reaction is activation controlled and is also complicated by reactant adsorption. Several limiting cases are treated. The method is compared with a method proposed earlier based on an intuitive hybrid equivalent circuit comprising the separate cases of either slow electron transfer or reactant adsorption is made and the limits of its validity are assessed. Application of the complete theory to Tl+ reduction showed that it proceeded by a CeC mechanism, complicated by both TI and Tl+ adsorption. The necessity of combining first- and second-order experimental data is stressed. The main reason for this is that the effects of adsorption and slow electron transfer tend to compensate each other. However, the presence of reactant adsorption raises the possibility of measuring unusually high electron transfer rate constants.