  Abelian potentials of pointlike moving sources are obtained from the
nonstandard theory of Yang--Mills field. They are used for the construction of
the time-symmetric and time-asymmetric Fokker-type action integrals describing
the dynamics of two-particle system with confinement interaction. The
time-asymmetric model is reformulated in the framework of the Hamiltonian
formalism. The corresponding two-body problem is reduced to quadratures. The
behaviour of Regge trajectories is estimated within the semiclassical
consideration.
