In this paper an attempt is made to study the thermoelectric power in quantum dots of non-parabolic semiconductors in the presence of a parallel magnetic field on the basis of a new electron dispersion law. It is found, taking Hg1 - xCdxTe and In 1 - xGaxAsyP1 - y lattice matched to InP as examples, that the thermoelectric power exhibits strong oscillatory dependencies with increasing magnetic field, alloy composition and thickness of the quantum dots, respectively. The thermopower increases with decreasing electron concentration and the numerical values of the same power in quaternary materials are greater in comparison with ternary compounds. © 1995.