Abstract Starting with the traditional Scheil–Cahn additivity principle, a new phenomenological method has been developed for the prediction of the progress of non-isothermal diffusional transformation processes. It is shown, that by formal generalization of the conventional additivity rule, various types of kinetic differential equations can be derived from the same isothermal kinetic law. This new approach is applied to the derivation of Avrami type generalized kinetic functions. They are suitable for the phenomenological description of anisothermal, diffusion-controlled, transformation processes. First, based on computer simulations, fundamental features of generalized kinetic functions derived from extended additivity principle are discussed. Next, practical feasibility of the approach has been demonstrated by estimating the start of austenite/ferrite transformation (i.e. incubation time) in a hypoeutectoid steel during continuous cooling.