A spatially one-dimensional model for the behaviour of flocculated suspensions in clarifier-thickeners is studied. This model combines a theory of sedimentation-consolidation processes of flocculated suspensions, which leads to a strongly degenerate diffusion equation, with the discontinuous flux appearing in the recently analyzed clarifier-thickener (CT) setup. This setup includes both clarification and thickening zones of clarifier-thickener units, while the earlier ideal continuous thickener (ICT) concept explicitly models the thickening zone only. The construction of steady-state concentration profiles attainable in a continuously operated CT is described. This construction incorporates an entropy principle, which implies that only those steady states are admissible for which the solids concentration is increasing downwards. Numerical examples of steady-state profiles and their applications to comparisons between both modes of operation, to the control of sediment height through selection of the clarification/thickening split ratio of the feed flux, and for capacity calculations are presented. A numerical example illustrates the use of a numerical method for the full (time-dependent) model to compare several fill-up strategies. (C) 2007 Elsevier B.V. All rights reserved.