Numerical simulations of protostars condensing out of turbulent interstellar gas clouds suggest that binary and multiple protostar systems are common. Such systems form from gas which has been strongly compressed and cooled in radiative shocks. Individual protostars result either from thermal fragmentation of extended layers, or from rotational fragmentation induced by accretion; they are much denser than their surroundings, well separated, and therefore likely to survive as separate entities.