Key points Cerebral haemodynamic response to neural stimulation has been extensively investigated in animal and clinical studies, in both adult and paediatric populations, but little is known about cerebral haemodynamic functional response in the fetal brain. The present study describes the cerebral haemodynamic response measured by near‐infrared spectroscopy to somatosensory stimulation in fetal sheep. The cerebral haemodynamic response in the fetal sheep brain changes from a positive (increase in oxyhaemoglobin (oxyHb)) response pattern to a negative or biphasic response pattern when the duration of somatosensory stimulation is increased, probably due to cerebral vasoconstriction with prolonged stimulations. In contrast to adult studies, we have found that changes in fetal cerebral blood flow and oxyHb are positively increased in response to somatosensory stimulation during hypercapnia. We propose this is related to reduced vascular resistance and recruitment of cerebral vasculature in the fetal brain during hypercapnia. Abstract Functional hyperaemia induced by a localised increase in neuronal activity has been suggested to occur in the fetal brain owing to a positive blood oxygen level‐dependent (BOLD) signal recorded by functional magnetic resonance imaging following acoustic stimulation. To study the effect of somatosensory input on local cerebral perfusion we used near‐infrared spectroscopy (NIRS) in anaesthetised, partially exteriorised fetal sheep where the median nerve was stimulated with trains of pulses (2 ms, 3.3 Hz) for durations of 1.8, 4.8 and 7.8 s. Signal averaging of cerebral NIRS responses to 20 stimulus trains repeated every 60 s revealed that a short duration of stimulation (1.8 s) increased oxyhaemoglobin in the contralateral cortex consistent with a positive functional response, whereas longer durations of stimulation (4.8, 7.8 s) produced more variable oxyhaemoglobin responses including positive, negative and biphasic patterns of change. Mean arterial blood pressure and cerebral perfusion as monitored by laser Doppler flowmetry always showed small, but coincident increases following median nerve stimulation regardless of the type of response detected by the NIRS in the contralateral cortex. Hypercapnia significantly increased the baseline total haemoglobin and deoxyhaemoglobin, and in 7 of 8 fetal sheep positively increased the changes in contralateral total haemoglobin and oxyhaemoglobin in response to the 7.8 s stimulus train, compared to the response recorded during normocapnia. These results show that activity‐driven changes in cerebral perfusion and oxygen delivery are present in the fetal brain, and persist even during periods of hypercapnia‐induced cerebral vasodilatation.