The explanation of the observed light neutrino flavour oscillations requires new particles, absent in the present theory of elementary particles, the so-called “Standard Model”. Extensions of the Standard Model where these new particles are within reach of collider experiments often feature a pair of additional "heavy neutrinos”, with nearly equal masses. Physicists from the University of Basel have recently shown that the small mass difference is predicted in simple neutrino mass theories of this type, and that it leads to oscillations between heavy neutrino states and heavy antineutrino states. These heavy neutrinos and antineutrinos can be detected by their decays into leptons and antileptons of the Standard Model. For comparatively long-lived heavy neutrinos, the oscillations could be resolved at the next (high-luminosity) stage of LHCb, and at envisioned future particle colliders. Their observation would allow a deep insight into the origin of neutrino masses (Mod. Phys. Lett. A34 (2019)).