Process for producing cellulolytic or hemicellulolytic enzymes comprising: - a phase a) of growth of a cellulolytic microorganism, said cellulolytic microorganism being a fungus of the species Trichoderma reesei, in a closed reactor, in the presence of at least one carbon growth substrate at a concentration of between 10 and 90 g/L, at a temperature of 25-30°C and a pH of 4-5.5, - a phase b) of production of enzymes, wherein at least one inducing carbon substrate is introduced at a temperature of 25-27°C and a pH of 4-5, process, wherein - said inducing substrate is a pretreated pomace originating from a process for the pretreatment of lignocellulosic material, said pretreatment being a steam explosion under acidic conditions, and said pomace not having been subjected to enzymatic hydrolysis and being introduced in fed-batch or continuous mode, - said pretreated pomace, in a suspension at ambient temperature at 10% by weight DM, has an apparent viscosity of less than 1 Pa·s for a shear rate of 10 s -1, preferably less than 0.15 Pa·s., - said pomace is introduced at a rate of between 0.3 and 0.8 grams DM per litre of medium and per hour in continuous mode; in fed-batch mode the amount of pomace added every f hours, f being between 0.5 h and 48 h, is between 0.3f and 0.8f grams of dry matter per litre of medium, - said pomace is formed from a liquid and a solid, the solid containing 20-70% of dry matter, of which 20-50% is lignin, 30-60% by weight is cellulose and 1-10% by weight is mineral compounds and hemicellulose, and the liquid containing 30-80% by weight of sugars in the form of xylose, xyloligosaccarides, mannose and arabinose. - a phase a) of growth of a cellulolytic microorganism, said cellulolytic microorganism being a fungus of the species Trichoderma reesei, in a closed reactor, in the presence of at least one carbon growth substrate at a concentration of between 10 and 90 g/L, at a temperature of 25-30°C and a pH of 4-5.5, - a phase b) of production of enzymes, wherein at least one inducing carbon substrate is introduced at a temperature of 25-27°C and a pH of 4-5, - said inducing substrate is a pretreated pomace originating from a process for the pretreatment of lignocellulosic material, said pretreatment being a steam explosion under acidic conditions, and said pomace not having been subjected to enzymatic hydrolysis and being introduced in fed-batch or continuous mode, - said pretreated pomace, in a suspension at ambient temperature at 10% by weight DM, has an apparent viscosity of less than 1 Pa·s for a shear rate of 10 s -1, preferably less than 0.15 Pa·s., - said pomace is introduced at a rate of between 0.3 and 0.8 grams DM per litre of medium and per hour in continuous mode; in fed-batch mode the amount of pomace added every f hours, f being between 0.5 h and 48 h, is between 0.3f and 0.8f grams of dry matter per litre of medium, - said pomace is formed from a liquid and a solid, the solid containing 20-70% of dry matter, of which 20-50% is lignin, 30-60% by weight is cellulose and 1-10% by weight is mineral compounds and hemicellulose, and the liquid containing 30-80% by weight of sugars in the form of xylose, xyloligosaccarides, mannose and arabinose.