We compared the relationship between the bispectral index and end‐tidal desflurane concentrations in 20 patients undergoing elective surgery. Patients received epidurally either 10 ml saline (group S) or 10 ml bupivacaine 0.125% with epinephrine 1/800 000 (group B) before induction of anaesthesia with sufentanil (0.15 μg.kg^−1^) and propofol (2 mg.kg^−1^); muscle relaxation was obtained with cisatracurium (0.2 mg.kg^−1^). Patients lungs were ventilated to maintain end‐tidal desflurane at 3% in O~2~/N~2~O (50/50) until 5 min after skin incision, followed by two consecutive 10 min periods at end‐tidal desflurane 6% and 9%. bispectral index values were recorded before induction, at 3% desflurane before and 5 min after skin incision, and at 6% and 9% end‐tidal desflurane. Bispectral index decreased with increasing end‐tidal desflurane concentration (anova: p < 0.05). The decrease in bispectral index was significant between pre‐induction, 3% and 6% desflurane. No significant difference was observed at 3% desflurane before and after skin incision, or between 6 and 9% desflurane. The relationship between bispectral index and end‐tidal desflurane concentration was fitted by a linear regression in each group. No significant difference in bispectral index was observed between the groups at any time. We conclude that bispectral index decreases with increasing desflurane concentration and that this relationship is not affected by epidural 0.125% bupivacaine.