The dynamical laws of classical physics, given in Chap. 2, can approximatively be retained for microscopic systems as well, but with restrictions of a new type. The basic goal is to impose discreteness onto the classical theory. We add discretization q-conditions to the otherwise unchanged classical canonical equations. The corresponding restrictions must be graceful in the sense that they must not modify the dynamics of macroscopic systems and they must not destroy the consistency of the classical equations.