Hydrogenic excited states of a 2D exciton are degenerate. In the presence of a weak magnetic field, the S-states with a zero momentum of the center of mass get coupled to the P-states with finite momentum of the center of mass. This field-induced coupling leads to a strong modification of the dispersion branches of the exciton spectrum. Namely, the lower branch acquires a shape of a “mexican hat” with a minimum at a finite momentum. At certain magnetic field, exciton branches exhibit a linear crossing, similarly to the spectrum of a 2D electron in the presence of spin–orbit coupling. While spin is not involved, degenerate S and P states play the role of the spin projections. Lifting of degeneracy due to diamagnetic shifts and deviation of electron–hole attraction from purely Coulomb suppresses the linear crossing.