We report a detailed investigation of fluorescence properties of synthetic eumelanin pigment in solution. A complete set of fluorescence spectra in the near-UV and visible range is analysed. Excitation spectra at a few selected emission energies are also investigated. Our measurements support the hypothesis that fluorescence in eumelanin is related to chemically distinct oligomeric units that can be selectively excited. Fluorescence due to large oligomer systems is spectrally differentiated from that due to monomers and small oligomer systems. Fluorescence excitation measurements show the contribution of 5,6-dihydroxyndole-2-carboxylic acid and 5,6-dihydroxyndole monomers to the emission of small-size oligomers.