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The theory of the two-dimensional (2D) magnetoexcitons was enlarged in two aspects. One of them takes into account the electron-hole (
e–h
) exchange Coulomb interaction, which appears when the conduction and the valence electrons belong partially to both bands. The exchange Coulomb interaction gives rise to the Dirac cone dispersion law in the range of small in-plane wave vectors
k
||
obeying to the condition |
k
||
|
l
0
< 1, where
l
0
is the magnetic length. Such dispersion law may change essentially the properties of the high density magnetoexcitons opening the possibility of their Bose-Einstein condensation at different from zero temperatures [1]. Another aspect concerns the high density magnetoexcitons with fractional filling factors in conditions of fractional quantum Hall effects. The Chern-Simons gauge field was introduced into the Hamiltonian of the 2D coplanar
e–h
system by the unitary transformation. It gives rise to the additional gauge vector potential, the influence of which leads to the anisotropic corrections to the magnetoexciton magnetic mass [2].