Enzymes behave differently when attached to solid supports for four main reasons: (1) their conformations when they are supported may differ from those in free solution, (2) they act upon substrates in a different environment, (3) there will be partitioning of substrate between the support and the free solution, and (4) there will be effects due to diffusion of the substrate in the support. The present paper examines effects (3) and (4) and shows how rates will vary with substrate concentration. If factors (1) and (2) do not enter, rates in the limit of high substrate concentrations will be the same for the supported enzyme as in free solution. At low substrate concentrations, rates will be less for the supported enzyme if the substrate is less soluble in the support than in free solution, and the apparent Michaelis constant,Km(app.), will be greater; conversely, for higher solubility in the support, rates will be greater andKm(app.) smaller. Effect (4) leads to lower rates and higherKm(app.) values, except in the limit of high substrate concentrations. At a sufficiently low thickness of the support, depending upon the activity of the enzyme, the kinetic behavior becomes identical with that in free solution.