  We discuss the impact of heavy neutrino-antineutrino oscillations (NNOs) on
heavy neutral lepton (HNL) searches at proposed electron-positron colliders
such as the future circular $e^+e^-$ collider (FCC-ee). During the $Z$ pole
run, HNLs can be produced alongside a light neutrino or antineutrino that
escapes detection and can decay into a charged lepton or antilepton together
with an off-shell $W$ boson. In this case, signals of lepton number violation
only show up in the final state distributions. We discuss how NNOs, a typical
feature of collider-testable low-scale seesaw models where the heavy neutrinos
form pseudo-Dirac pairs, modify such final state distributions. For example,
the forward-backward asymmetry (FBA) of the reconstructed heavy (anti)neutrinos
develops an oscillatory dependence on the HNL lifetime. We show that these
oscillations can be resolvable for long-lived HNLs. We also discuss that when
the NNOs are not resolvable, they can nevertheless significantly modify the
theory predictions for FBAs and observables such as the ratio of the total
number of HNL decays into $\ell^-$ over ones into $\ell^+$, in an interval of
the angle~$\theta$ between the HNL and the beam axis. Our results show that
NNOs should be included in collider simulations of HNLs at the FCCee.
