The pre-main-sequence evolution of a rotating non-magnetic star is investigated. Stars forming out of interstellar gas clouds are shown to have sufficient angular momentum to cause centrifugal force to balance gravity before reaching the stable Hayashi phase, so that during subsequent evolution matter must be left behind from the equatorial regions. During contraction through the fully convective Hayasbi phase the coupling of central and surface regions by convection determines a definite rotation law which we take to be uniform rotation. YVith continued contraction the star develops a radiative core and the "viscosity" effect of the turbulence is no longer operative; each element of the growing core therefore conserves its angular momentum causing an inward increase in angular velocity. It is shown that the ratio of centrifugal force to gravity increases in the central regions and that for stars with mass > 0.8 Mo rotational instability is likely to occur. This is imagined to cause the splitting of the original star into two components and so form a binary system. Assuming conservation of angular momentum on fission it is shown that stars with mass 4 Mo can form a contact binary system whereas more massive stars will produce separated binaries. The theoretical limits of Mo and 4 Mo for the total mass of contact binanes are in good agreement with observations of V Ursae ajoris systems, as is the distribution of total angular momentum with mass.