Strongly coupled plasmon-exciton systems offer promising applications in nanooptics. The classification of the coupling regime is currently debated both from experimental and theoretical perspectives. We present a method to unambiguously identify strong coupling in plasmon-exciton core-shell nanoparticles by measuring true absorption spectra of the system. We investigate the coupling of excitons in J-aggregates to the localized surface plasmon polaritons on gold nanospheres and nanorods by fine-tuning the plasmon resonance via layer-by-layer deposition of polyelectrolytes. While both structures show a characteristic anticrossing in extinction and scattering experiments, the careful assessment of the systems' light absorption reveals that strong coupling of the plasmon to the exciton is only present in the nanorod system. In a phenomenological model of two classical coupled oscillators, intermediate coupling strengths split up only the resonance frequency of the light-driven oscillator, while the other one still dissipates energy at its original frequency. Only in the strong-coupling limit, both oscillators split up the frequencies at which they dissipate energy, qualitatively explaining our experimental finding.The electromagnetic coupling of molecular excitations to plasmonic nanoparticles offers a promising method to manipulate the light-matter interaction at the nanoscale. This approach is frequently used to enhance the optical cross-section of molecules, e.g. in surface enhanced Raman scattering (SERS) [1], enhancement of fluorescence [2] and infrared absorption [3,4], plasmonenhanced light-harvesting in dye-sensitized solar cells [5] or plasmon-enhanced dye-lasers [6].The coupling strength between molecular excitations and plasmons is given by the rate of energy-exchange between the two components Ω = E · µ/h [7]. Here µ describes the transition dipole moment of the emitter and E the electric-field strength of the light at the emitter-location. Plasmonic nanoparticles foster exceptionally high coupling strengths, due to their capacity to strongly concentrate the light-field to sub-wavelength mode volumes and hence to generate very high electrical field-strengths in their vicinity. A particularly interesting coupling regime occurs, if the coupling increases to a level such that Ω surpasses all damping rates in the system. In this socalled strong coupling regime hybrid light-matter states emerge, which cannot be divided into separate light and matter components. The new resonances of the coupled system emerge from the plasmon resonance ω p and the exciton resonance ω ex as [8,9] where g is the coupling parameter.Hence, the presence of the new hybrid-states can be de- The most frequently used approach for achieving strong light-matter coupling on nanoparticles, is the fabrication of hybrid core-shell particles with a noble-metal core and a molecular shell. Several hybrid nanoparticles that allegedly show strong coupling have been presented in recent literature [14][15][16][17][18]. In several cases these claim...