A process for the production of cellulases and hemicellulases using a strain of a filamentous fungus in a stirred and aerated bioreactor, in at least two phases, a phase a) for growth of said strain in the presence of at least one carbonaceous growth substrate in a closed reactor, a phase b) for the continuous production of cellulases, in which at least one carbonaceous inducer substrate is supplied at a supply rate which is constant over a period of at least more than 200 h, said carbonaceous substrate being at least one aqueous hemicellulosic hydrolysate solution obtained from an acid pre-treatment of a lignocellulosic substrate, said aqueous hemicellulosic hydrolysate solution not undergoing prior sterilization and not undergoing pH rectification, being operated at a dilution rate in the range 0.001 to 0.02 h−1.