The present invention relates to a process for obtaining cellulose or a mixture containing at least cellulose and at least lignocellulose from at least one substrate that is at least to some extent amenable to fermentation comprising at least the steps of (1) to (3) and optionally (4), namely conversion of the substrate via addition of at least one inorganic base into an aqueous mixture with pH≥8.5 (step 1), ultrasound treatment of the aqueous mixture obtained after step (1) (step 2), separation of the aqueous mixture obtained after step (2) into a liquid aqueous phase and a disperse mixture containing, cellulose or a mixture containing at least cellulose and at least lignocellulose (step 3) and optionally purification of the disperse mixture obtained after step (3) containing cellulose or of the mixture containing at least cellulose and at least lignocellulose (step 4), where step (1) and step (2) of the process respectively are carried out at a temperature