10-20E

Two modified versions of the dipole model with a pair of mediating fields are considered. First modification affects the Yukawa term in the Lagrangian. In the second version non-linear self-action term is added. By constructing exact solutions of the field equations with the use of a covariant Green function we derive a Lagrangian with many-point time-nonlocal interaction terms. For the linear dipole model the two-particle interaction, in the non-relativistic limit, is shown to be a sum of Coulomb and linear confinement terms. For the nonlinear $\varphi^3$--model the interactions are shown to include pairwise potentials and also three-particle cluster potentials with logarithmic confinement. Approaches towards a consistent relativistic treatment of the models are proposed, and the problem of divergences is discussed.