It is tentatively suggested that SO galaxies belong to two (possibly o
verlapping) populations. One of these contains mainly luminous oblate
objects that are truly intermediate between ellipticals and spirals. T
he other population of SO galaxies appears to consist of fainter, pred
ominantly prolate objects. Evidence for this conclusion is based on th
e observation that the luminosity function of SO galaxies appears to c
ontain a faint component that is not, or only weakly, present among E
and Sa galaxies. The objects belonging to this faint population have a
distribution of apparent axial ratios that is even flatter than that
observed for galaxies of type Sc. This suggests that this population o
f faint flattened objects is mainly composed of predominantly prolate
galaxies. Alternatively it might be assumed that SO galaxies, on avera
ge, become more triaxial towards lower luminosities.