Pituitary hormones are released in pulses as a result of episodic patterns of electrical activity in neuroendocrine neurons. The mechanisms underlying such pulsatility have, however, been difficult to elucidate. For example, the luteinizing hormone-releasing hormone neurons regulating reproductive functioning have a sparse and scattered distribution within the hypothalamus which has made definitive electrophysiological investigation impracticable. Little is known not only of their electrical characteristics, but also of the critical neural components with which they interact to form the so-called "luteinizing hormone-releasing hormone pulse generator". We have used here a neural modelling approach, based on the FitzHugh-Nagumo model of a single neuron, to provide a simple dynamical network model of this neuroendocrine pulse generator. We have found that the minimal components required to generate pulsatile luteinizing hormone secretion arise from combining luteinizing hormone-releasing hormone neurons with reciprocally connected inhibitory interneurons and an external stimulatory input. Local GABA neurons and ascending noradrenergic and/or adrenergic inputs have been used as the biological basis for these respective components. The network displays a wide repertoire of behaviours comparable with experimental observations, including some thought previously to be paradoxical. The capacity of this model network to display complex behavioural features interpretable against experimental evidence suggests that this type of modelling may become a necessary adjunct to empirical studies of pulsatile neuroendocrine systems.