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We give examples on how to distinguish whether a particle is self-conjugate or not. For light active neutrinos, neutrinoless double beta decay is the main method to do this. However, alternative mechanism for the decay exist, and may make a definite answer difficult. In the presence of interactions beyond V-A, neutrino-electron scattering may provide an answer. Finally, we ask whether the self-conjugacy of dark matter can be determined by direct detection only.