  We study the NGS (Non--dissipative Gravitational Singularity) model, which
successfully describes the non--linear stage of evolution of perturbations (see
[1], [2] and references therein). This model predicts DM density distribution
$\rho(r) \sim r^{-\alpha}$ with $\alpha \simeq 1.8$ which holds from very small
distances $r_{\rm min} \simeq 0.01~{\rm pc}$ up to very large distances $r_{\rm
max} \simeq 5~{\rm Mpc}$. Assuming the neutralino to be a CDM particle, we
calculate the annihilation of neutralinos in the vicinity of the singularity
(Galactic Center). If neutralinos are the dominant component of DM in our
Galaxy, the produced energy is enough to provide the whole observed activity of
the GC. Neutralinos of the most general composition and of mass in the range
$20~{\rm GeV} \leq m_\c \leq 1~{\rm TeV}$ are considered. We find the
neutralino compositions which give the relic density needed for the Mixed Dark
Matter (MDM) model and we evaluate for these compositions the high--energy
($E_{\gamma} > 100 ~{\rm MeV}$) gamma--ray flux under the constraint that the
radio flux is lower than the observational limit. The compositions with the
detectable gamma--ray flux which we found are provided by a set of almost pure
gaugino states with the neutralino mass between $100$ and $500$ GeV. We
demonstrate that a detectable high--energy gamma--ray flux is produced by the
neutralino annihilation also in the case when neutralinos provide a small
fraction (down to $0.1 \%$) of the DM in our Galaxy. The predicted flux is
$F_\gamma \sim 10^{-7}-10^{-8}~{\rm cm}^{-2}~{\rm s}^{-1}$ for $E_\gamma \gsim
300~{\rm MeV}$
