The intra- and inter-band relaxation dynamics of CdSe/CdS/ZnS core/shell/shell quantum dots are investigated with the aid of time-resolved nonlinear transmission spectra which are obtained using femtosecond pump-probe technique. By selectively exciting the core and shell carrier, the dynamics are studied in detail. Carrier relaxation is found faster in the conduction band of the CdS shell (about 130 fs) than that in the conduction band of the CdSe core (about 400 fs). From the experiments it is distinctly demonstrated the existence of the defect states in the interface between the CdSe core and the CdS shell, indicating that ultrafast spectroscopy might be a suitable tool in studying interface and surface morphology properties in nanosystems.