Premature infants have immature respiratory control that predisposes them to apnoea, haemoglobin oxygen desaturation and bradycardia. Apnoeas are loosely classified, according to the presence or absence of respiratory effort, into central, obstructive or mixed. There are a variety of conditions, in the perioperative period, that predispose an infant to apnoea, including: central nervous system (CNS) lesions, infections and sepsis, ambient temperature fluctuations, cardiac abnormalities, metabolic derangements, anaemia, upper airway structural abnormalities, necrotising enterocolitis, drug administration (including opiates and general anaesthetics) and possibly gastro-oesophageal reflux. Various monitoring techniques are discussed; the mainstay are pulse oximetry and abdominal-pressure transduction. There is some evidence of both short- and long-term complications of repeated apnoeas in the neonatal period, but the causal relationship is difficult to establish. Continuous positive airway pressure and caffeine therapy (up to 10 mg kg(-1)) are the most common treatments of neonatal apnoea. The less soluble volatile agents and regional anaesthetic techniques (without concurrent sedation) are associated with a lower incident of postoperative apnoea.