Relevant electrochemical processes present rate equations with non-unity reaction orders. For such reactions, an analytical treatment is developed for the stationary voltammetric response and the surface concentrations at the rotating disc electrode and at microelectrodes of any shape, as frequently/preferably employed to reveal their electrode kinetics. The expressions deduced are applicable when one or both redox species are initially present and cover any degree of reversibility. From the general solution obtained, the limit cases of fully reversible and irreversible reactions are derived. By linearizing the current-potential response of the former, the reaction orders can be determined, as well as the value of the reversible half-wave potential that strikingly depends on whether one or both species are initially present in contrast with the case of unity orders. For irreversible processes, the linearization of the complete current-potential response is also possible and it enables us to extract the reaction order and the half-wave potential. An expression for the latter is given as a function of the heterogeneous rate constant and the mass transport coefficient. Additional protocols of kinetic analysis are discussed on the basis of Tafel and Koutecký-Levich-like plots.