  We present a hadronic model of activity for Galactic gamma-ray-loud binaries,
in which the multi-TeV neutrino flux from the source can be much higher and/or
harder than the detected TeV gamma-ray flux. This is related to the fact that
most neutrinos are produced in pp interactions close to the bright massive
star, in a region optically thick for the TeV gamma-rays. Considering the
specific example of LS I +61o 303, we derive upper bounds for neutrino fluxes
from various proton injection spectra compatible with the observed
multi-wavelength spectrum. At this upper level of neutrino emission, we
demonstrate that ICECUBE will not only detect this source at 5 sigma C.L. after
one year of operation, but, after 3 years of exposure, will also collect a
sample marginally sufficient to constrain the spectral characteristics of the
neutrino signal, directly related to the underlying source acceleration
mechanisms.
