  Several families of nonlinear field equations are known to possess space-
localized singularity-free solutions which describe fields with finite
Hermitian norms. This paper studies the interaction of such fields with given
electromagnetic potentials entering the field's equations through the covariant
derivative form. The main result is: the motion of a space-localized field, as
a whole, is essentially identical to that of a point charge moving in the same
electromagnetic potentials, if this field is a solution either to a nonlinear
Schrodinger or to a nonlinear Dirac equation, under some very general and
physically meaningful assumptions. Using an alternative method, similar result
is shown to hold for a very wide class of nonlinear field equations.
