Stationary models for cool rapidly rotating neutron stars are construc
ted. Axially symmetric case in Newtonian approximation is considered a
nd general relativity effects are evaluated. The chosen barotropic equ
ation 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 ob
tained which provide loss of dynamical stability of the star (fragment
ation) when the ratio of rotational energy to gravitational energy bet
a > 0.27, and which are allowed for a collapsing star; in this region
one may expect two-stage collapse and explosion to occur. Ln particula
r, it is shown that these conditions are fulfilled for a collapsing ir
on-oxygen stellar core with a mass of 2M. which is described by a soli
d-body rotating polytrope n = 3 having a maximum possible angular velo
city and being marginally stable relative to the collapse.