The branching pattern of the conducting airways is significantly asymmetrical in the human, and even more so in other species. Although this asymmetry is believed to have an important effect on air flow and other transport processes in the bronchial tree, both experimental and theoretical studies have predominantly employed symmetrical model bifurcations. In this paper, published morphometric data for four species (human, dog, rat and hamster) is used to calculate the frequencies with which different degrees of asymmetry occur, and to examine the relationships between four of its manifestations, asymmetry of the cross-sectional areas, the lengths, the branching angles and the flow rates of the daughter branches. The observed characteristics are compared with some of the theoretical 'branching laws' which have been proposed. Quantification of the correlations between the different manifestations of asymmetry allows the geometrical characteristics to be specified for a range of realistic asymmetrical bifurcations, for use in either theoretical or experimental studies of transport in the bronchial tree.