  It is shown that the Schr\"{o}dinger nonrelativistic equation of a system of
interacting particles is not a rigorously nonrelativistic equation since it is
based on the implicit assumption of finiteness of the interaction propagation
velocity. For a system of interacting particles, a fully nonrelativistic
nonlinear system of integro-differential equations is proposed. In the case
where the size of the system of particles is of the same order as the Compton
wavelength associated with particles, certain essential differences are shown
to exist as compared with traditional consequences of the nonrelativistic
Schr\"{o}dinger equation.
