We present the first search for bosonic super-WIMPs as keV-scale dark matter candidates performed with the GERDA experiment. GERDA is a neutrinoless double-beta decay experiment which operates high-purity germanium detectors enriched in $^{76}$Ge in an ultra-low background environment at the Laboratori Nazionali del Gran Sasso (LNGS) of INFN in Italy. Searches were performed for pseudoscalar and vector particles in the mass region from 60 keV/c$^2$ to 1 MeV/c$^2$. No evidence for a dark matter signal was observed, and the most stringent constraints on the couplings of super-WIMPs with masses above 120 keV/c$^2$ have been set. As an example, at a mass of 150 keV/c$^2$ the most stringent direct limits on the dimensionless couplings of axion-like particles and dark photons to electrons of $g_{ae} < 3 cdot 10^{-12}$ and ${alpha}/{alpha} < 6.5 cdot 10^{-24}$ at 90% credible interval, respectively, were obtained.
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