  A classical mechanics of two Coulomb charges on a plane $(e_1, m_1)$ and
$(e_2, m_2)$ subject to a constant magnetic field perpendicular to a plane is
considered. Special "superintegrable" trajectories (circular and linear) for
which the distance between charges remains unchanged are indicated as well as
their respectful constants of motion. The number of the independent constants
of motion for special trajectories is larger for generic ones. A classification
of pairs of charges for which special trajectories occur is given. The special
trajectories for three particular cases of two electrons, (electron -
positron), (electron - $\alpha$-particle) are described explicitly.
