Collisional–radiative models were originally developed to model the competition between collisional excitation and radiative decay under circumstances in which neither is dominant. However, in the context of fusion plasma physics, collisional–radiative models are now often used to separate plasma components into ‘slow’ and ‘fast’ species, so that only the collisional–radiatively determined time development of the slow species need be considered explicitly. This paper extends this idea to the description of plasmas which contain molecules. In order to do so it makes a rather thorough (and some might say, boring) analysis of the requirements of a valid collisional–radiative model, and derives a new set of validity criteria, which are not related to the equilibrium time–scales. These criteria can also be used to generate all possible collisional–radiative models for a given set of plasma rate processes. Details of how this is done and an analysis of the situation that applies when molecular hydrogen is present in the plasma are presented.