  A search for rare decays of gadolinium isotopes was performed with an
ultra-low background high-purity germanium detector at Gran Sasso Underground
Laboratory (Italy). A 198 g Gd$_2$O$_3$ powder sample was measured for 63.8 d
with a total Gd exposure of 12.6 kg$\times$d. $^{152}$Gd is the most promising
isotope for resonant neutrinoless double electron capture which could
significantly enhance the decay rate over other neutrinoless double beta decay
processes. The half-life for this decay was constrained to $>4.2\times10^{12}$
yr (90\% credibility). This limit is still orders of magnitude away from
theoretical predictions but it is the first established limit on the transition
paving the way for future experiments. In addition, other rare alpha and double
beta decay modes were investigated in $^{152}$Gd, $^{154}$Gd, and $^{160}$Gd
with half-life limits in the range of $10^{17-20}$ yr.
