This paper deals with the kinetic study of reaction mechanisms with enzyme inactivation induced by a suicide substrate in the presence or absence of an auxiliary substrate and in conditions of excess of substrates in relation to the enzyme concentration and vice versa. A transient-phase approach has been developed that enables explicit equations with one or two significant exponentials to be obtained, thereby showing the dependence of product concentration on time. The validity of these equations has been checked, and a comparison made with those previously obtained by other authors. We propose an experimental design to determine the corresponding parameters and kinetic constants. The simplicity of our method allows a systematic application to more complex mechanisms.