Diagnosis of sleep-disordered breathing is based on the presence of an abnormal breathing pattern during sleep. In this study, an algorithm was developed for the offline breath-to-breath analysis of the nocturnal respiratory recordings. For that purpose, respiratory signals (nasal airway pressure, thoracic and abdominal movements) were divided into half waves using period amplitude analysis. Individual breaths were characterized by the parameters of the half waves (duration, amplitude, and slope). These values can be used to discriminate between normal and abnormal breaths. This algorithm was applied to six polysomnographic recordings to distinguish abnormal breathing events (apneas and hypopneas). The algorithm was robust for the identification of breaths (sensitivity = 96.8%, positive prediction value (PPV) = 99.5%). The detection of apneas and hypopneas was compared to the manual scoring of two experienced sleep technicians: sensitivity was, respectively, 89.2 and 88.9%, PPV was 54.1 and 59.3%. The classification of apneas into central, obstructive, or mixed was in concordance with the observers in 68% of the apneas. Although the algorithm tended to detect more hypopneas than the clinical standard, this study shows that the extraction of breath-to-breath parameters is useful for detection of abnormal respiratory events and provides a basis for further characterization of these events.