We report on the preparation and structural characterization of CdSe nanocrystals, which are covered by a multishell structure from CdS and ZnS. By using the newly developed successive ion layer adhesion and reaction (SILAR) technique, we could gradually change the shell composition from CdS to ZnS in the radial direction. Because of the stepwise adjustment of the lattice parameters in the radial direction, the resulting nanocrystals show a high crystallinity and are almost perfectly spherical, as was investigated by X-ray diffraction and electron microscopy. Also, due to the radial increase of the respective valence- and conduction-band offsets, the nanocrystals are well electronically passivated. This leads to a high fluorescence quantum yield of 70-85% for the amine terminated multishell particles in organic solvents and a quantum yield of up to 50% for mercapto propionic acid-covered particles in water. Finally, we present experimental results that substantiate the superior photochemical and colloidal stability of the multishell particles.