Two-stage treatments of Eucalyptus globulus wood were carried out in HCl-acetic acid-water media in order to obtain high-purity cellulose pulps. The effects of selected operational variables affecting the first pulping stage on the yield and composition of delignified solids were determined. A pulp selected from this study was used as substrate for a further pulping stage, which was carried out either at the normal boiling temperature or at 130 °C under a variety of conditions. This method was found to be particularly suitable for obtaining pulps with low hemicellulose contents.