  We simulate the neutrino and $\gamma$-ray emissions of the Galaxy which are
originated from the hadronic scattering of cosmic rays (CR) with the
interstellar medium (ISM).
  Rather than assuming a uniform CR density, we estimate the spatial
distribution of CR nuclei by means of numerical simulations. We consider
several models of the galactic magnetic field and of the ISM distribution
finding only a weak dependence of our results on their choice. We found that by
extrapolating the predicted $\gamma$-ray spectra down to few GeV we get a good
agreement with EGRET measurements. Then, we can reliably compare our
predictions with available observations above the TeV both for the
$\gamma$-rays and the neutrinos. We confirm that the excesses observed by
MILAGRO in the Cygnus region and by HESS in the Galactic Centre Ridge cannot be
explained without invoking significant CR over-densities in those regions.
Finally, we discuss the perspectives that a km$^3$ neutrino telescope based in
the North hemisphere has to measure the diffuse emission from the inner Galaxy.
