This article presents a method for evaluating the intrinsic kinetic parameters of the specific substrate utilization rate (r) equation and discusses the results obtained for anaerobic sludge-bed samples taken from a horizontal-flow anaerobic immobilized sludge (HAIS) reactor. This method utilizes a differential reactor filled with polyurethane foam matrices containing immobilized anaerobic sludge which is subjected to a range of feeding substrate flow rates. The range of liquid superficial velocities thus obtained are used for generating data of observed specific substrate utilization rates (r(obs)) under a diversity of external mass transfer resistance conditions. The r(obs) curves are then adjusted to permit their extrapolation for the condition of no external mass transfer resistance, and the values determined are used as a test for the condition of absence of limitation of internal mass transfer. The intrinsic parameters r(max), the maximum specific substrate utilization rate, and K-S, the half-velocity coefficient, are evaluated from the r values under no external mass transfer resistance and no internal mass transfer limitation. The application of such a method for anaerobic sludge immobilized in polyurethane foam particles treating a glucose substrate at 30 degrees C resulted in intrinsic r(max) and K-S, respectively, of 0.330 mg chemical oxygen demand (COD) . mg(-1) volatile suspended solids (VSS) . h(-1) and 72 mg COD . L(-1). In comparison with the values found in the literature, intrinsic r(max) is significantly high and intrinsic K-S is relatively low.