  Possibilities for detecting heavy Majorana neutrinos ($N$'s) at future
$e{\mu}$ colliders are investigated. In contrast to the $e^-e^+$ colliders
(LEP200 and NLC), the center-of-mass (CMS) energies achieved at $e{\mu}$
colliders can be much higher and the $Z$-mediated $s$ channel is excluded
automatically. This opens the attractive possibility of having high production
cross sections for $N$'s and at the same time probing only the strength of
charged current couplings of $N$'s ($NWe$ and $NW{\mu}$). The production cross
sections and the expected numbers of events for the reaction $e^{\mp}
{\mu}^{\pm} \to NN \to W^{\pm} {\ell}^{\mp} W^{\pm} {\ell}^{\prime \mp}$ are
calculated for various masses $M$ of the Majorana neutrinos and for the CMS
energies $\sqrt{s} = 0.5-6.0$ TeV. The values of the charged current coupling
parameters are set equal to their present upper bounds. We obtain reasonably
high production cross sections. Further, the effects of the off-shell
intermediate $N$'s turn out to be significant only at $\sqrt{s}
\stackrel{>}{\approx} 2$ TeV.
