Method for producing cellulolytic enzymes in xylose-containing hydrolysates for degradation of lignocellulose-containing biomasses, comprising the steps of: a) providing a genetically modified filamentous fungal strain having the ability to overexpress cellobiohydrolases, endoglucanases, exocellulases and/or β-glucosidases in xylose-containing substrates as production medium, the natural promoters of which have been replaced by a xylanase promoter, b) cultivating the genetically modified filamentous fungal strain under non-limiting conditions in the hydrolysate to form biomass in a first phase, c) setting growth-limiting conditions in a subsequent second phase, so that the fungal strain produces the expressed cellulolytic enzymes without itself growing or propagating, d) isolating the cellulolytic enzymes produced in step c), characterized in that - the cultivation of the genetically modified filamentous fungal strain under growth-limiting conditions takes place in a trickle flow method in a fixedbed reactor, with use of solid bodies having surfaces which are coverable by the fungal strain, so that the fungal mycelium grows on the solid bodies and so that, furthermore, the expression of the cellulolytic enzymes is induced by xylose, - the genetically modified filamentous fungal strain is an auxotrophic mutant which requires a specific growth factor for growth, - the growth-limiting conditions are established by withdrawal of the growth factor, and - the production of the cellulolytic enzymes is enhanced by overexpression of a transcription activator. a) providing a genetically modified filamentous fungal strain having the ability to overexpress cellobiohydrolases, endoglucanases, exocellulases and/or β-glucosidases in xylose-containing substrates as production medium, the natural promoters of which have been replaced by a xylanase promoter, b) cultivating the genetically modified filamentous fungal strain under non-limiting conditions in the hydrolysate to form biomass in a first phase, c) setting growth-limiting conditions in a subsequent second phase, so that the fungal strain produces the expressed cellulolytic enzymes without itself growing or propagating, d) isolating the cellulolytic enzymes produced in step c), characterized in that - the cultivation of the genetically modified filamentous fungal strain under growth-limiting conditions takes place in a trickle flow method in a fixedbed reactor, with use of solid bodies having surfaces which are coverable by the fungal strain, so that the fungal mycelium grows on the solid bodies and so that, furthermore, the expression of the cellulolytic enzymes is induced by xylose, - the genetically modified filamentous fungal strain is an auxotrophic mutant which requires a specific growth factor for growth, - the growth-limiting conditions are established by withdrawal of the growth factor, and - the production of the cellulolytic enzymes is enhanced by overexpression of a transcription activator. - the cultivation of the genetically modified filamentous fungal strain under growth-limiting conditions takes place in a trickle flow method in a fixedbed reactor, with use of solid bodies having surfaces which are coverable by the fungal strain, so that the fungal mycelium grows on the solid bodies and so that, furthermore, the expression of the cellulolytic enzymes is induced by xylose, - the genetically modified filamentous fungal strain is an auxotrophic mutant which requires a specific growth factor for growth, - the growth-limiting conditions are established by withdrawal of the growth factor, and - the production of the cellulolytic enzymes is enhanced by overexpression of a transcription activator. <EOS>