A pseudo-first-order catalytic mechanism in which both reactant and product of a redox reaction are strongly immobilized on an electrode surface is theoretically analysed under conditions of square-wave (SWV) and staircase cyclic voltammetry (SCV). A mathematical procedure is developed under diffusionless conditions. The relationships between the properties of the voltammetric response and both the kinetic parameters of the redox reaction and the parameters of the excitation signal are studied. The phenomenon of the quasi-reversible maximum is discussed. A comparative study between SWV and SCV is presented and the limitations and advantages of both techniques, from analytical and kinetic points of view, are discussed. The theoretical predictions are experimentally confirmed by the redox reaction of azobenzene in the presence of hydrogen peroxide as an oxidizing agent.