Numerical calculations have been made for the early stages of collapse of an axisymmetric cloud, both with and without rotation. The results show that, in the absence of rotation, deviations from spherical symmetry do not usually grow as the cloud collapses; instead, pressure forces remain sufficient to maintain rough spherical symmetry and prevent the cloud from fragmenting during its collapse. Fragmentation can occur, but usually only if the initial configuration is already unstable to fragmentation. In the presence of rapid rotation, however, the central part of the cloud always appears to condense into a rotating ‘ doughnut ’ or ring with a density minimum at the centre. Such a rotating ring is almost certainly unstable and will presumably fragment into two or more condensations orbiting around each other. The formation in this way of a binary or multiple system of stars would largely resolve the classical ‘ angular momentum problem ’ and might account for the fact that most stars are in fact found in binary or multiple systems; even the single stars might be accounted for as escapers from unstable multiple systems.