Strongly coupled plasmon-exciton hybrid nanostructures are fabricated and their optical properties are studied. The plasmonic and excitonic systems are gold nanoshells and J-aggregates, respectively. Gold nanoshells are tunable plasmonic core-shell nanoparticles which can sustain distinct dipole and quadrupole plasmons with resonant energies dependent on core-size/shell-thickness ratio. J-aggregates are organic semiconducting material with excitons that possess very high oscillator strength making them suitable for coherent interaction with other kinds of excitations. The J-aggregates are formed on the surface of the nanoshells when a water/ethanol (50:50) solution of the dye molecules (2,2'-dimethyl-8-phenyl-5,6,5',6'-dibenzothiacarbocyanine chloride) is added to an aqueous solution of nanoshells. These nanoshell-J-aggregate complexes exhibit coherent coupling between localized plasmons of the nanoshell and excitons of the molecular J-aggregates. Coherent coupling strengths of 120 meV and 100 meV have been measured for dipole and quadrupole plasmon interactions with excitons, respectively. Femtosecond time-resolved transmission spectroscopy studies are carried out in order to understand the possible sources of optical nonlinearities in the nanoshell-J-aggregate hybrid. Transient absorption of the interacting plasmon-exciton system is observed, in dramatic contrast to the photoinduced transmission of the pristine J-aggregate. An additional, transient Fano-shaped modulation within the Fano dip is also observable. The transient behavior of the J-aggregate-Au nanoshell complex is described by a combined one-exciton and two-exciton state model coupled to the nanoshell plasmon.