Аннотация:Stationary models for cool rapidly rotating neutron stars are constructed. Axially symmetric case in Newtonian approximation is considered, and general relativity effects are evaluated. The chosen barotropic equation of state and rotation law determine state of the star at a given mass M and angular momentum J. The region of parameters M and J is obtained which provide loss of dynamical stability of the star (fragmentation) when the ratio of rotational energy to gravitational energy beta greater than 0.27, and which are allowed for a collapsing star; in this region, one may expect two-stage collapse and explosion to occur. In particular, it is shown that these conditions are fulfilled for a collapsing iron-oxygen stellar core with a mass of 2 solar masses which is described by a solid-body rotating polytrope n = 3 having a maximum possible angular velocity and being marginally stable relative to the collapse.