Whitehead claims to have inaugurated a Copernican revolution in the domain of theory of process: The overturn of the notion of a processes' “subject” by the notion “superject”, invented to discribe a reality in process as the result of its own proceeding, while referring to the processes' field. Whitehead's approach encourages to realize that every empirical research on proceeding realities presupposes models, which illustrate what is meant by saying 'process'. Such models, and their corresponding theory, are general patterns, which determine how one constitutes empirical views about reality, which - henceforth - shall be the object of research. One constitutes only actual models of empirical reality, which are covered by the general model one already has and which is to be brought, for the sake of scientificity, to outspoken awareness. Such a general model, as a system of descriptions, is only complete, when it is structured by a theory, explaining its functioning. Trying a hylomorphistic approach, I refer to an Aristotelean-Thomist tradition to furnish a model, theory and terminology for the description of what we call 'process' as a particular state of a proceeding being and its empirical encounter with the scientist, who is charged to do research about it.