We discuss a ∼ 3 σ signal (local) in the light Higgs-boson search in the diphoton decay mode at ∼ 96 GeV as reported by CMS, together with a ∼ 2 σ excess (local) in the bb final state at LEP in the same mass range. We interpret this possible signal as a Higgs boson in the 2 Higgs Doublet Model with an additional real Higgs singlet (N2HDM). We find that the lightest Higgs boson of the N2HDM can perfectly fit both excesses simultaneously, while the second lightest state is in full agreement with the Higgs-boson measurements at 125 GeV, and the full Higgs-boson sector is in agreement with all Higgs exclusion bounds from LEP, the Tevatron and the LHC as well as other theoretical and experimental constraints. We show that only the N2HDM type II and IV can fit both the LEP excess and the CMS excess with a large ggF production component at ∼ 96 GeV. We derive bounds on the N2HDM Higgs sector from a fit to both excesses and describe how this signal can be further analyzed at the LHC and at future e + e − colliders, such as the ILC.SM is the Minimal Supersymmetric Standard Model (MSSM) [19,20]. In contrast to the single Higgs doublet of the SM, the MSSM by construction, requires the presence of two Higgs doublets, Φ 1 and Φ 2 . In the CP conserving case the MSSM Higgs sector consists of two CP-even, one CP-odd and two charged Higgs bosons. The light (or the heavy) CP-even MSSM Higgs boson can be interpreted as the signal discovered at ∼ 125 GeV [21] (see Refs. [22,23] for recent updates). However, in Ref. [22] it was demonstrated that the MSSM cannot explain the CMS excess in the diphoton final state.Going beyond the MSSM, a well-motivated extension is given by the Next-to-MSSM (NMSSM) (see [24,25] for reviews). The NMSSM provides a solution for the so-called "µ problem" by naturally associating an adequate scale to the µ parameter appearing in the MSSM superpotential [26,27]. In the NMSSM a new singlet superfield is introduced, which only couples to the Higgs-and sfermion-sectors, giving rise to an effective µ-term, proportional to the vacuum expectation value (vev) of the scalar singlet. In the CP conserving case the NMSSM Higgs sector consists of three CP-even Higgs bosons, h i (i = 1, 2, 3), two CP-odd Higgs bosons, a j (j = 1, 2), and the charged Higgs boson pair H ± . In the NMSSM not only the lightest but also the second lightest CP-even Higgs boson can be interpreted as the signal observed at about 125 GeV, see, e.g., [28,29]. In Ref. [17] it was found that the NMSSM can indeed simultaeneously satisfy the two excesses mentioned above. In this case, the Higgs boson at ∼ 96 GeV has a large singlet component, but also a sufficiently large doublet component to give rise to the two excesses.A natural extension of the NMSSM is the µνSSM, in which the singlet superfield is interpreted as a right-handed neutrino superfield [30,31] (see for reviews). The µνSSM is the simplest extension of the MSSM that can provide massive neutrinos through a see-saw mechanism at the electroweak scale. A Yukawa coupling for right-handed ne...