  This is a paper about induced gamma emission. The X-ray electron-nuclear
double transitions (XENDT) are processes in which a transition effected by an
inner atomic electron takes place simultaneously with a nuclear electromagnetic
transition. We give expressions for the cross sections of electric and magnetic
XENDTs of various multipole orders. We calculate the rate of deexcitation of
isomeric nuclei induced by XENDTs for the case when the holes in the atomic
shells are produced by incident ionizing electrons and find that the induced
nuclear deexcitation rate becomes comparable to the natural decay rate for
ionizing fluxes of the order of $10^{14}$ W cm$^{-2}$. We show that for E1 and
M1 nuclear processes for which there is a matching between the electron and the
nuclear transition energies, the XENDTs can be used to produce pulses of
M\"{o}ssbauer radiation, with yields of the order of $10^4$ Bq mA$^{-1}$.
