Growth, substrate and phenolic compound biodegradation by Penicillitum decumbens was studied on vinasses. This fungus was selected because of its tolerance to the phenolic compounds present in this waste. The biodegradation process of vinasses was researched in batch regime by conducting experiments where the initial concentration of substrate and phenolic compounds were 42.6 g COWL and 0.21 g gallic acid/L, respectively. This fungus significantly degraded the total phenolic compounds in vinasses aerobically without the need for any nutrient supplements in the medium. A maximum value of phenols removal of 74% was achieved after 3 days ' treatment. P. decumbens produces a decolourization of the vinasses from the 1st day of incubation. Higher reductions in colour were achieved between the 4th and 5th days of treatment, the best result being 41 % of the initial colour removed after 4 days ' treatment. A mathernatical model based on three differential equations was formulated to describe this biodegradation process assuming that a fraction of the organic content of vinasses is non-biodegradable. The proposed equations were validated by comparing the theoretical curves obtained with the corresponding experimental data of substrate and biomass concentrations. The small deviations obtained in both cases (lower than 5%) demonstrated the suitability of the mathematical model proposed and suggested that this model very accurately described the variation of substrate and biomass concentrations with time in the aerobic degradation process of vinasses with P. decumbens and that the parameters obtained represent the activity of this microorganism effecting the aerobic degradation of this waste. Finally, the biomass yield coefficient was found to be 0.35 g VSS/g COD through the relationship between the amount of cells produced and substrate uptake. This value coincides with that obtained theoretically from the mathematical model formulated. (c) 2005 Elsevier Ltd. All rights reserved.