  In this paper, we use analytical methods to study the last stages of the
double neutron star (NS) system evolution. Depending on the initial masses of
the components, this evolution can occur either in the framework of the merging
scenario or in the NS stripping model. The main new ingredient of this work,
compared with the previous calculations, is accounting for accretion spin-up of
the massive component. This effect leads to a significant decrease in the
duration of the stable mass transfer of matter in the stripping mechanism.
Within the framework of the Newtonian approximation, we determine the mass
boundary between the merging and stripping scenarios. It is shown that this
boundary weakly depends on the total mass of the system and the specific form
of the NS equation of state and is determined mainly by the initial mass ratio
of the components. The stripping scenario is realized at M2/M1<0.8, so it
should make a large contribution to the population of close to us gravitational
wave events from NS-NS coalescing binaries and accompanying short gamma-ray
bursts. Nevertheless, the value obtained requires further clarification, taking
into account relativistic effects, possible non-conservative mass transfer,
etc.
