Abstract This paper is the first of a series devoted to strong interaction theory. As a general introduction to the series, we give a critical survey of theories and models presently in force. In a previous paper, we studied the kinematics of a single unstable hadron, the state of which was described as an incoherent superposition of states with different masses. To such a state there corresponds a function on the Poincaré group, called a characteristic function. Here we take up these old results anew, we work them out, and we go more thoroughly into their physical foundations. Then we describe the kinematics of several particles. The theory of strong interactions must take into account two opposed features of unstable hadrons: their identity and their difference with stable hadrons. The identity implies that an unstable hadron is in a certain state, described by a density operator; the difference is that this state has a mass spectrum, whose width cannot be neglected. We make the further assumption that the state is an incoherent superposition of components with different masses. This assumption is compared to the statistics experiment of Baton and Laurens, in which the components with different masses have been effectively separated. We define the characteristic function of such a state, and we point out its analogy with a usual characteristic function in probability theory. The physical meaning of characteristic functions is studied on the example of a spin, then in the general case. Then we study the characteristic function of several hadrons, and we define two notions: the global particle and the inclusive characteristic function.