  Neutrinoless double electron capture is a process that, if detected, would
give evidence of lepton number violation and the Majorana nature of neutrinos.
A search for neutrinoless double electron capture of $^{36}$Ar has been
performed with germanium detectors installed in liquid argon using data from
Phase I of the GERmanium Detector Array (GERDA) experiment at the Gran Sasso
Laboratory of INFN, Italy. No signal was observed and an experimental lower
limit on the half-life of the radiative neutrinoless double electron capture of
$^{36}$Ar was established: $T_{1/2} > $ 3.6 $\times$ 10$^{21}$ yr at 90 % C.I.
