  The Next-to-Minimal Supersymmetric Standard Model (NMSSM) offers a rich
framework embedding physics beyond the Standard Model as well as consistent
interpretations of the results about the Higgs signal detected at the LHC. We
investigate the decays of neutral Higgs states into Standard Model (SM)
fermions and gauge bosons. We perform full one-loop calculations of the decay
widths and include leading higher-order QCD corrections. We first discuss the
technical aspects of our approach, before confronting our predictions to those
of existing public tools, performing a numerical analysis and discussing the
remaining theoretical uncertainties. In particular, we find that the decay
widths of doublet-dominated heavy Higgs bosons into electroweak gauge bosons
are dominated by the radiative corrections, so that the tree-level
approximations that are often employed in phenomenological analyses fail.
Finally, we focus on the phenomenological properties of a mostly singlet-like
state with a mass below the one at $125\,$GeV, a scenario that appears commonly
within the NMSSM. In fact, the possible existence of a singlet-dominated state
in the mass range around or just below $100\,$GeV would have interesting
phenomenological implications. Such a scenario could provide an interpretation
for both the $2.3\sigma$ local excess observed at LEP in the $e^+e^-\to Z(H\to
b\bar{b})$ searches at $\sim 98\,$GeV and for the local excess in the diphoton
searches recently reported by CMS in this mass range, while at the same time it
would reduce the "Little Hierarchy" problem.
