  The remnant resulting from the merger of two neutron stars produces neutrinos
in copious amounts. In this paper we present the neutrino emission results
obtained via Newtonian, high-resolution simulations of the coalescence event.
These simulations use three-dimensional smoothed particle hydrodynamics
together with a nuclear, temperature dependent equation of state and a
multi-flavour neutrino leakage scheme. We present the details of our scheme,
discuss the neutrino emission results from a neutron star coalescence and
compare them to the core-collapse supernova case where neutrino emission has
been studied for several decades. The average neutrino energies are similar to
those in the supernova case, but contrary to the latter, the luminosities are
dominated by electron-type antineutrinos which are produced in the hot,
neutron-rich, thick disk of the merger remnant. The cooler parts of this disk
contain substantial fractions of heavy nuclei, which, however, do not influence
the overall neutrino emission results significantly. Our total neutrino
luminosities from the merger event are considerably lower than those found in
previous investigations. This has serious consequences for the ability to
produce a gamma-ray burst via neutrino annihilation. The neutrinos are emitted
preferentially along the initial binary rotation axis, an event seen
``pole-on'' would appear much brighter in neutrinos than a similar event seen
``edge-on''.
