The electron energy structure of linear artificial molecules and one-dimensional chains formed of spherical semiconductor nanocrystals is investigated with and without an applied magnetic field. Both uniform and multilayer nanocrystals are studied. The calculations are performed within the effective mass model by numerically integrating the effective mass equation on a two-dimensional cylindrical grid. Some calculations are, for comparison, performed also in the tight-binding approach. Density contours are presented to illustrate the transformation of states in systems of strongly interacting coupled quantum dots. Strong interaction between the quantum-dot-quantum-well structures in a chain of nanocrystals can lead to the formation of a very narrow ground-state miniband, well separated from the excited levels with the energies almost independent of the magnetic field. (C) 2003 American Institute of Physics.