  We study neutrino energy emission rates (emissivities) due to electron
bremsstrahlung produced by $ee$ and $ep$ collisions in the superfluid neutron
star cores. The neutrino emission due to $ee$ collisions is shown to be the
dominant neutrino reaction at not too high temperatures ($T \la 10^8$ K) in
dense matter if all other neutrino reactions involving nucleons are strongly
suppressed by neutron and proton superfluidity. Simple practical expressions
for the $ee$ and $ep$ neutrino emissivities are obtained. The efficiency of
various neutrino reactions in the superfluid neutron-star cores is discussed
for the cases of standard neutrino energy losses and the losses enhanced by the
direct Urca process.
