  The problem of spectra formation in hydrodynamic approach to A+A collisions
is considered within the Boltzmann equations. It is shown analytically and
illustrated by numerical calculations that the particle momentum spectra can be
presented in the Cooper-Frye form despite freeze-out is not sharp and has the
finite temporal width. The latter is equal to the inverse of the particle
collision rate at points $(t_{\sigma}({\bf r},p),{\bf r})$ of the maximal
emission at a fixed momentum $p$. The set of these points forms the
hypersurfaces $t_\sigma({\bf r},p)$ which strongly depend on the values of $p$
and typically do not enclose completely the initially dense matter. This is an
important difference from the standard Cooper-Frye prescription (CFp), with a
common freeze-out hypersurface for all $p$, that affects significantly the
predicted spectra. Also, the well known problem of CFp as for negative
contributions to the spectra from non-space-like parts of the freeze-out
hypersurface is naturally eliminated in this improved prescription.
