Theoretical calculations, utilizing the effective-mass theory, are presented of exciton energies in semiconductor core-shell and quantum-dot-quantum-well nanocrystals. For core-shell nanocrystals, the influence of diffusion on the transition energies is investigated. It is shown that the diffusion-induced blue shift of the transition energy is a nonmonotonic function of the nanocrystal radius, and that the Coulomb interaction energy of the exciton is a strong function of the diffusion time. The calculations also show that the intersublevel energy spacing is a nonmonotonic function of the ground-state interband transition energy. For quantum-dot-quantum-well nanocrystals, both the exciton transition energy and the overlap integral between the electron and hole wave function is calculated. It is shown that quantum-dot-quantum-well nanocrystals can be designed such that the overlap integral either increases or decreases with increasing amounts of diffusion. (C)>2002 American Institute of Physics.