  A general analysis of the three-vertex loop amplitude in a strong magnetic
field, based on the asymptotic form of the electron propagator in the field, is
performed. In order to investigate the photon-neutrino process gamma gamma ->
nu bar nu, the vertex combinations of the scalar-vector-vector (SVV),
pseudoscalar-vector-vector (PVV), 3-vector (VVV), and
axial-vector-vector-vector (AVV) types are considered. It is shown that only
the SVV amplitude grows linearly with the magnetic field strength, while in the
other amplitudes, PVV, VVV, and AVV, the linearly growing terms are cancelled.
The process gamma gamma -> nu bar nu is investigated in the
left-right-symmetric extension of the standard model of electroweak
interaction, where the effective scalar nu nu e e coupling could exist.
Possible astrophysical manifestations of the considered process are discussed.
