This thesis is concerned with the detection of apnoeas in infants from an abdominal breathing signal, where an apnoea is a pause in breathing during sleep. Apnoea detection is performed by analysing breathing signals recorded during sleep studies. An abdominal breathing signal recorded by the BabyLog polysomnographic system is used for this research. A reference set of apnoeas is formed by three human experts identifying apnoeas five seconds and longer within ten overnight recordings of breathing. There was a 10% disagreement on the identification of events. Based on this reference set, the performances of existing methods of apnoea detection were evaluated, and found to have low incidence of false negatives but high incidence of false positives. An existing algorithm was developed, and an application of this algorithm as part of a study of low risk infants is presented. Properties that represent most apnoeas as found in an abdominal breathing signal are described. Human experts are consulted to determine what properties of the signal they use to recognise apnoeas, and a collection of deterministic, or shape, properties is condensed to represent expert opinion. An apnoea is modeled as a flat region with four properties: flatness, duration, thinness and smoothness. Mathematical descriptions that discriminate between apnoea and non-apnoea events of each property are formulated. An expert system for the classification of events is then developed, based on property measures being classified by a neural network. The system has achieved 95% to 98% accuracy for a false detection rate of 15% to 40%. Applications include scoring apnoeas for sleep studies, an aid to clinicians in diagnosing breathing problems, and developing standard definitions of breathing signals corresponding to apnoeas.