The influence of the Rashba spin-orbit coupling on the two-dimensional (2D) electrons and holes in a strong perpendicular magnetic field leads to different results of the Landau quantization in different spin projections. In Landau gauge the unidimensional wave vector describing the free motion in one in-plane direction is the same for both spin projections, whereas the numbers of the Landau quantization levels are different. For electron in s-type conduction band they differ by one, as was established earlier by Rashba¹, whereas for heavy holes in p-type valence band influenced by the 2D symmetry of the layer they differ by three. There are two lowest spin-splitted Landau levels for electrons as well as two lowest for holes. They give rise to four lowest energy levels of the 2D magnetoexcitons. It is shown that two of them are dipole-active in band-to-band quantum transitions, one is quadrupole-active and the fourth is forbidden. The optical orientation under the influence of the circularly polarized light leads to optical alignment of the magnetoexcitons with different orbital momentum projections on the direction of the external magnetic field