Magnocellular oxytocin neurones, found mainly in the supraoptic nucleus and in the paraventricular nucleus of the hypothalamus, project their axons to the posterior pituitary, from where they secrete oxytocin into the bloodstream. Oxytocin is well known for its essential role in breastfeeding and for facilitating labour. However, in the last decades oxytocin has also been recognised to have roles in energy balance and osmotic pressure balance. During breastfeeding and labour, the spiking activity of oxytocin neurones alternates between long periods of slow basal activity and a few seconds of bursting, when oxytocin neurones fire synchronously at up to 100 spikes per second. Energy and osmotic pressure balance are associated with small to medium linear alterations of the basal activity of oxytocin neurons. A computational model was developed to simulate the spiking activity of oxytocin neurones described in the literature. The simulations mimicked their basal activity, their response to cholecystokinin (CCK), a gut peptide involved in energy balance, and their spiking response to osmotic pressure. However, the final product of oxytocin neurones is the secreted oxytocin and its plasma concentration. Thus, it was developed a secretion model matched to experimental data in the literature, coupled it with the spiking model, and added a model for oxytocin clearance from plasma. That allowed simulating the plasma oxytocin response to CCK and to changes in the osmotic pressure. In addition, the model offered important insights. It supports the necessity of a depolarization after potential (DAP) in some oxytocin neuron membranes, the essential role of inhibitory inputs during the oxytocin osmotic response, a new mechanism for partially explaining oxytocin response to hypovolemia, and explains the role of the after hyperpolarizing (AHP) current as a filter of synaptic inputs to oxytocin neurones.