Two 8‐month‐old Suffolk sheep, weighing 45 and 55 kg, respectively, were anaesthetised for an intrathalamic injection of an experimental drug. After an uneventful procedure and general anaesthesia using controlled mechanical ventilation, the sheep were weaned off the ventilator and allowed to breathe spontaneously with end‐tidal carbon dioxide (PE′CO2) levels remaining within normal limits. During recovery, intermittent apnoeic phases were observed with increasing PE′CO2 (>70 mmHg) and decreasing oxygen saturation of haemoglobin (SpO2) levels (90%–91%). The sheep appeared unresponsive, and reflexes were absent. This alternated with phases of normal mentation, normal reflexes and regular spontaneous ventilation, where ventilatory parameters improved. Tentative treatment to reduce intracranial pressure and administration of the opioid receptor antagonist naloxone were unsuccessful. Definite diagnosis of Cheyne–Stokes respiration is difficult but was suspected in these two cases; cerebral cortex damage, intracranial haemorrhage or opioid mediated respiratory rhythm disturbances are possible causes.