The mineralization of low concentrations of phenol and glucose by Penicillium sp., Fusarium oxysporum, and Rhizoctonia sp. was measured in liquid culture. At concentrations of TO to 500 ng per ml, the rate constant of mineralization of phenol by Penicillium sp. decreased with a lowering of the initial substrate concentration. The lower the inoculum density, the lower was the maximum rate of mineralization of 3 g of phenol ml−1 and the longer the acclimation period. The curves of mineralization of phenol by Penicillium sp. and of low of glucose by F. oxysporum and Rhizoctonia sp. were usually fitted best by the logistic and not the first-order model of the Monod family of kinetic m logistic model also provided the best fit to data depicting mineralization of phenol by Penicillium sp. inoculated into sterile sand. The parameters estimated by the logistic model, however, were not always consistent with the measurements. Thus, this form of the logistic model derived from the Monod equation, originally developed for bacteria, may not be appropriate for describing the biodegradation of organic compounds by filamentous fungi. © 1990, British Mycological Society. All rights reserved.