The picosecond time-resolved Stokes shift of the laser dye, coumarin 480 (I) is studied in neutral (Triton X-100, TX), cationic (cetyltrimethylammonium bromide, CTAB), and anionic (sodium dodecyl sulfate, SDS) micelles. Above critical micellar concentration (cmc) for all three micelles I exhibits wavelength dependent fluorescence decays and a distinct growth at the long wavelengths. The time dependent Stokes shift studies indicate that the water molecules in the Stern layer of the micelles relax on the time scale 180-550 ps, which is slower than the subpicosecond relaxation dynamics observed in ordinary bulk water.