A mathematical model to describe the kinetics of enzyme production by the filamentous fungus Trichoderma harzianum P49P11 was developed using a low cost substrate as main carbon source (pre-treated sugarcane bagasse). The model describes the cell growth, variation of substrate concentration and production of three kinds of enzymes (cellulases, beta-glucosidase and xylanase) in different sugarcane bagasse concentrations (5; 10; 20; 30; 40 g L-1). The 10 g L-1 concentration was used to validate the model and the other to parameter estimation. The model for enzyme production has terms implicitly representing induction and repression. Substrate variation was represented by a simple degradation rate. The models seem to represent well the kinetics with a good fit for the majority of the assays. Validation results indicate that the models are adequate to represent the kinetics for a biotechnological process. (C) 2015 Elsevier Ltd. All rights reserved.