Allometric equations on wing dimensions versus body mass are given for eight species of megabats and 76 species of microbats, on forearm length versus mass for 14 species of megabats and 90 species of microbats, and on lower leg length versus mass for 11 species of megabats and 45 species of microbats. Megabats have, on average, shorter wing span, small wing area, higher wing loading and lower aspect ratio than have frugivorous microbats and the insectivorous vespertilionids of similar mass. Vespertilionids have the longest span, largest wing area and lowest wing loading in relation to body mass of the bat groups for which regression lines were calculated (megabats, frugivorous microbats, vespertilionids, molossids), characteristics that are important for slow flight and manoeuvrability for insect capture. Molossids have the highest wing loading of the groups. There is a weak tendency towards higher aspect ratio for larger bats than for smaller ones (positive slope). The slopes for most characters fit geometric similarity or have confidence intervals including the value for geometric similarity. Only in three cases does the slope lie nearer that for elastic similarity: for the forearm in nycterids and emballonurids and the lower leg length in molossids. Also in these cases the confidence intervals are wide and include the value for elastic similarity and that for geometric similarity as well. In megabats the slope for the lower leg length is much steeper than for geometric similarity. The slope for the forearm length is rather similar to that for wing span in the various groups. Megabats and frugivorous microbats have rather similar slopes for all the characters measured, but differ from the other groups only in wing area, wing loading and aspect ratio. The two frugivorous bat groups also have about the same elevation of the regression lines for aspect ratio and forearm length. Megabats and frugivorous microbats thus show a close convergence in wing area, wing loading, aspect ratio and forearm length. The regression equations provide `norms' for the respective bat groups. Those species that deviate 10% or more from the mean trends for wing measurements are divided into different groups, based on the wing's aspect ratio and loading. Bats with low aspect ratio wings usually have large pinnae, which improve the ability to discover small objects such as insects on leaves. Families or species of bats with wings of low aspect ratio are, for instance, Megadermatidae, Nycteridae, Rhinolophus ferrumequinum (Rhinolophidae), Chrotopterus auritus (Phyllostomidae) and Plecotus (Vespertilionidae). The group with average aspect ratio wings contains bats with different kinds of flight style and foraging behaviour, for instance many pteropodids, phyllostomids and vespertilionids. Bats with high aspect ratio wings are, for instance, Molossidae, Rhynchonycteris naso (Emballonuridae) and Nyctalus leisleri (Vespertilionidae). The regression lines for wing span, area and loading in megabats lie almost in the region of the lines for Greenewalt's (1975) passeriform group, whereas the span and area for vespertilionid bats are larger and the wing loading much smaller than for most birds of similar mass. Molossid bats have a larger relative wing span and aspect ratio than have most birds, and a wing area and loading similar to those of small birds of the passeriform group. Vespertilionid bats have about the same aspect ratio as birds of the passeriform group, whereas megabats have somewhat lower ratios. Molossid bats show strong convergence with swifts and swallows in foraging behaviour and in wing form. Similar convergences can be found between various vespertilionid bats, flycatchers and swallows.