The energy structure of one-dimensional chains of spherical nanocrystals is investigated. Both, uniform and multilayer nanocrystals are studied. Calculations are performed with the k(.)p method and the envelope function approximation (EFA). The valence subband mixing is accounted for by considering a four-band Hamiltonian. The high (spherical) symmetry of the building blocks leads to a unique energy structure with miniband widths depending on the z-component of the angular momentum. These minibands are (2L + 1) quasi-degenerated in the low-coupling regime, L being the quantum number of the angular momentum. The magnetic field splits quasidegeneracy leading to a mixture of successive narrow and wide minibands. The ground miniband of chains built of antidots becomes very narrow in the strong coupling regime and separates from the rest of the spectrum, so that a strong luminescence red-shift is predicted.