The cell-density distribution, associated with the slow growth of cells immobilized within a hollow-fiber or packed-bed reactor, is solved for various kinetics of substrate consumption. Approximate and numerical solutions, for first-order kinetics, show that the total cell mass grows at half the specific rate of free cells when substrate diffusion is growth limiting. This integral property, as well as the spatial distribution of substrate concentration and cell density, are approximately similar to those of zero-order kinetics, for which a simple analytical solution exists. Similar features are simulated for other positive-order (e.g. Monod) kinetics. Self-inhibitory kinetics of substrate consumption may lead to a nonmonotonic profile of cell-density and to multiple growth solutions.