Absorption spectra of chemically synthesized uniform and multilayer semiconductor nanocrystals in a magnetic field are investigated theoretically. The nanocrystals are modelled by spherical barrier/well potentials. The electron states are calculated within the effective mass model. A four-band k p Hamiltonian, accounting for the valence subband mixing, is used to obtain the hole states. The magneto-optical transition spectrum depends strongly on the size and composition of the nanocrystals. In the case of small uniform quantum dots, only the linear Zeeman splitting of the electron and hole energy levels is observed even for very strong magnetic fields. In larger nanocrystals, the quadratic magnetic interaction turns out to be important and the transition spectrum becomes complicated. The most complicated influence of the magnetic field is found in quantum dot–quantum well systems in which the lowest electron and hole states are localized in a thin spherical layer. It is shown that transitions that are optically active when no magnetic field is applied remain strong even in very strong fields.