Three-dimensional hydrodynamical, Newtonian calculations of the coalescence of equal-mass binary neutron stars are performed, including a physical high-density equation of state and a treatment of the neutrino emission of the heated matter. The total neutrino luminosity climbs to a maximum value of 1--$1.5cdot 10^{53}$~erg/s of which 90--95% originate from the toroidal gas cloud surrounding the very dense core formed after the merging. When the neutrino luminosities are highest, $ ubar u$-annihilation deposits about 0.2--0.3% of the emitted neutrino energy in the immediate neighborhood of the merger, and the maximum integral energy deposition rate is 3--$4cdot 10^{50}$~erg/s. Since the $3,M_{odot}$ core of the merged object will most likely collapse into a black hole within milliseconds, the energy that can be pumped into a pair-photon fireball is insufficient by a factor of about 1000 to explain $gamma$-ray bursts at cosmological distances with an energy of the order of $10^{51}/(4pi)$~erg/steradian. Analytical estimates show that the additional energy provided by the annihilation of $ ubar u$ pairs emitted from a possible accretion torus of $sim 0.1,M_{odot}$ around the central black hole is still more than a factor of 10 too small, unless focussing of the fireball into a jet-like expansion plays an important role. About $10^{-4}$--$10^{-3}$~$M_odot$ of material lost during the neutron star merging and swept out from the system in a neutrino-driven wind might be a site for nucleosythesis. Aspects of a possible r-processing in these ejecta are discussed.
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