Based on the investigation of additive kinetic differential equations it is shown that the concept of the traditional isokinetic hypothesis defined by Christian can be easily generalized. By introducing the notion of the weakly isokinetic process, it is verified that the extended isokinetic model can be expressed in terms of an integro-differential equation. A special property of this integro-differential equation is that its right-hand side includes such state-parameters, which are determined by the whole temperature history (i.e. each state parameter is a functional of the time-temperature function, or any other selected state functions). © EDP Sciences.