  We study the decay $K_L -> e\mu$ in minimal extensions of the Standard Model
based on the gauge groups $SU(2)_L x U(1)_Y$ and $SU(2)_R x SU(2)_L x
U(1)_{B-L}$, in which heavy Majorana neutrinos are present. In $SU(2)_L x
U(1)_Y$ models with chiral neutral singlets, $B(K_L -> e\mu )$ cannot be much
larger than $5 x 10^{-15}$ without violating other low-energy constraints. In
$SU(2)_L x SU(2)_R x U(1)_{B-L}$ models, we find that heavy-neutrino-chirality
enhancements due to the presence of left-handed and right- handed currents can
give rise to a branching ratio close to the present experimental limit $B(K_L
-> e \mu)< 3.3 x 10^{-11}$.
