The Neugebauer equations and the Demichel equations on which they are based are one of the basic tools for modeling colour printing systems that use the halftoning technique, However, these equations implicitly assume that the colour ink distributions in the screen superposition are statistically independent. We show that this condition is not satisfied in the conventional screen superposition used for colour printing, and we discuss the consequences of this fact. Furthermore, we give a precise criterion that determines, for any number of superposed regular screens, in which cases the Demichel (and hence the Neugebauer) equations ave satisfied, and in which cases they fail: The Demichel equations fail in all cases where the screen superposition is singular; and they are satisfied in all nonsingular screen superpositions. We illustrate our results with several examples of both cases.