A model of the simple chemostat which allows for growth on the wall (or other marked surface) is presented as three nonlinear ordinary differential equations. The organisms which are attached to the wall do not wash out of the chemostat. This destroys the basic reduction of the chemostat equations to a monotone system, a technique which has been useful in the analysis of many chemostat-like equations. The adherence to and shearing from the wall eliminates the boundary equilibria. For a

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... y general model, the basic properties of invariance, dissipation, and uniform persistence are established. For two important special cases, global asymptotic results are obtained. Finally, a perturbation technique allows the special results to be extended to provide the rest point as a global attractor for nearby growth functions.