  The radiative decay of the massive neutrino $\nu_i \rightarrow \nu_j \gamma$
is investigated in the framework of the Standard Model in external
electromagnetic fields of various configurations: constant crossed field,
constant uniform magnetic field, plane monochromatic wave's field. The effect
of significant enhancement of the neutrino decay probability by the external
field (electromagnetic catalysis) is discussed. An especially strong
enhancement occurs in the case of the ultrarelativistic neutrino decay, since
in this case the decay probability does not contain suppression caused by the
smallness of the decaying neutrino mass. The ultrarelativistic neutrino decay
catalysis is significant even in a relatively weak external field ($F/F_e <<
1$, where $F_e$ is the critical Schwinger value). The expression for the photon
splitting probability into the neutrino pair $\gamma \rightarrow \nu_i
\bar\nu_j$ in the wave field is given. The estimations of a number of
gamma-quanta produced in a volume filled with an electromagnetic field and the
neutrino lifetime in a strong magnetic field are presented.
