The so-called no-interaction theorem of D.G. Currie, T.F.Jordan, E,C,S
udarshan, H.Leutwyler, G.Marmo and N,Mukunda makes it possible to cons
truct relativistic quasi-classical particle dynamics in the post-Galil
ean approximation only. We found that in this approximation the Lagran
gians are singular on some surfaces of the phase space. The dynamical
properties are essentially peculiar on the singular surfaces which we
studied. It is shown in this paper that in the case of rectilinear mot
ion of two electrons, the so-called ''radius of electron'' (the minima
l distance between the particles) can be interpreted as the dynamical
property of motion on the singular surface generated by the Lagrangian
of Darwin.