  The lepton-number violating process e p \to nu_e l l' X mediated by Majorana
neutrinos is studied for the HERA collider for (l l') = (e tau), (mu tau), (mu
mu) and (tau tau). Only the muonic decay of the tau is considered. The direct
limit on the effective muon Majorana mass, <m_{mu mu}> is improved
significantly to 4.0 times 10^3 GeV and for the first time direct limits on the
analogous effective masses connected with the tau sector are given, namely 4.2
times 10^3 GeV for <m_{e tau}>, 4.4 times 10^3 GeV for <m_{mu tau}> and 2.0
times 10^4 GeV for <m_{tau tau}>. We find that a more general analysis for an
upgraded HERA could improve this values by a factor of up to 40, yet still
being orders of magnitude worse than indirect limits.
