We study the neutrino emissivity of strongly magnetized neutron stars due to the charged and neutral current couplings of neutrinos to baryons in strong magnetic fields. The leading order neutral current process is the one-body neutrino-pair bremsstrahlung, which does not have an analogue in the zero field limit. The leading order charged current reaction is the known generalization of the direct Urca processes to strong magnetic fields. While for superstrong magnetic fields in excess of
G the direct Urca process dominates the
one-body bremsstrahlung, we find that for fields on the order
G and temperatures a few times K the one-body bremsstrahlung is the
dominant process. Numerical computation of the resulting emissivity, based on a
simple parametrization of the equation of state of the -matter in a strong
magnetic field, shows that the emissivity of this reaction is of the same order
of magnitude as that of the modified Urca process in the zero field limit.