  We estimate the fluxes of very high energy (VHE) gamma-rays and neutrinos
from the Galactic Center which are by-products of the hadronic interactions
between primary protons which are accelerated up to $\sim 10^{19}$eV and
ambient matter. We find that these signals depend strongly on the spectrum
index of the primary protons. This means that detection of these signals from
the Galactic Center will constrain the spectrum of the primary particles,
which, in turn, should constrain the acceleration mechanism at the Galactic
Center. We show that GeV-TeV gamma-rays will be detected by the ground-based
Cherenkov telescopes such as CANGAROOIII and the next-generation satellites
such as GLAST. Thus the acceleration region of the CRs below $\sim 10^{19}$eV
will be determined accurately by gamma-ray telescopes, which should help our
understanding on the particle acceleration. We estimate the event rate of VHE
neutrinos for the planned 1 km$^{2}$ detectors such as IceCube, ANTARES and
NESTOR. The event rate also depends on the spectrum index of the primary
protons. In the optimistic case, the event rate amounts to $\sim 10^4$ events
per year and the signals from the Galactic Center dominate the atmospheric
neutrino background.
