  We hunt for and discuss manifestly CP-violating effects which are mediated by
Majorana phases. These phases are present if the Standard Model neutrinos are
Majorana particles. We argue that while Majorana phases do affect the strength
of neutrinoless double beta decay (a well known fact), they do so in a way that
involves no manifest violation of CP. The conditions for manifestly
CP-violating phenomena -- differences between the rates for CP-mirror-image
processes -- are presented, and three examples are discussed: (i)
neutrino-antineutrino oscillation; (ii) rare decays of K and B mesons and their
antiparticles and (iii) the lepton asymmetry generated by the decay of
hypothetical very heavy right-handed "see-saw" neutrinos. We also find that,
for the case of degenerate light neutrinos, manifestly CP-violating effects in
neutrino-antineutrino oscillation vanish, although flavor-changing transitions
do not. Finally, we comment on leptogenesis with degenerate right-handed
neutrinos, and contrast it to the neutrino-antineutrino oscillation case.
