A 36-year-old woman and a 49-year-old man with symptoms of an obstructive sleep-apnoea syndrome benefited insufficiently from the therapy of choice, i.e. treatment with continuous positive airway pressure. Minor surgical procedures to improve the upper airways did not have the desired effect. Subsequently, maxillo-mandibular osteotomy was performed. Thereafter, both the daytime somnolence and the snoring during sleep disappeared. Indications for osteotomy of the maxilla and mandible are: failure of conservative therapy or other forms of treatment with a lower morbidity, severe mandibular hypoplasia, extreme respiratory distress and morbid obesity. Ventral displacement of the maxilla or mandible eliminates the obstruction at the level of the base of the tongue. The operation is successful for the first year in 95% of the patients. A disadvantage is the temporary post-operative morbidity.