  We discuss the prospects of detecting the processes
$e^+p\to\bar\nu_e\ell^+\ell'^+X$ and $\nu_ep\to e\ell^+\ell'^+X$
($\ell,\ell'=e,\mu,\tau$) under the conditions of the present $ep$ collider
HERA and of future colliders. These high-energy processes are assumed to be
mediated by the exchange of heavy Majorana neutrinos (HMN). We consider two
simple scenarios for the HMN mass spectrum: the effective singlet ($m_1\ll
m_2<m_3...$) and the effective doublet ($m_1<m_2\ll m_3...$). For the latter
case, the cross section includes information about CP-violating phases.
