Evolutionary processes of a polydisperse assemblage of particles in metastable or reactive surroundings are studied with allowance for the back influence of the assemblage upon the transient properties of the surroundings. Each particle either grows or reduces in size due to mass and heat exchange with the ambient medium in which it is immersed, the growth or reduction rate being given in a sufficiently general form as a function of both the particle size and the state of the medium. However, there is no generation of nuclei that give rise to new particles and the external supply to, or the forced withdrawal of particles from, the system are left out of the account. A mathematical model to deal with such processes is put forward, which is based on the kinetic equation for the particle population density and on mass and heat conservation equations for the system as a whole. The model can be generalized to situations when the particles are not distributed over their radius but over another relevant physical character : Examples of the application of the model to assemblages involved in evolution processes of different physical origin lead to very simple final formulae which agree well with experimental findings.