Eucalyptus globulus wood samples were subjected to fractionation at 110°C using acetic acid solutions with small quantities of HCl as catalyst. The effects of time (in range 5–6 h), acetic acid concentration (70–95%) and catalyst concentration (0-0.2%) on yield and composition of delignified samples were evaluated. A second-order incomplete factorial design was used to develop mathematical models capable of providing quantitative predictions, which were confirmed by further experimentation. The extreme values predicted for the dependent variables were: yield, 92-46%; lignin content, 24-6%; polysaccharide content, 87-56%; glucan/polysaccharides ratio, 0·97-0·78. The yield and the lignin content of samples were mainly influenced by the catalyst concentration. The polysaccharide content depended on both HCl and acetic acid concentrations. The glucan/polysaccharides ratio increased when the concentrations of HCl or acetic acid increased. The duration of treatments was not a significant variable in the range tested. The models predicted 86% delignification with 30% polysaccharides dissolved if the wood was treated with a liquor containing 95% acetic acid and 0·2% HCl.