  We show that (specifically scaled) equations of shear-free null geodesic
congruences on the Minkowski space-time possess intrinsic self-dual, restricted
gauge and algebraic structures. The complex eikonal, Weyl 2-spinor,
$SL(2,\mathbb C)$ Yang-Mills and complex Maxwell fields, the latter produced by
integer-valued electric charges ("elementary" for the Kerr-like congruences),
can all be explicitly associated with any shear-free null geodesic congruence.
Using twistor variables, we derive the general solution of the equations of the
shear-free null geodesic congruence (as a modification of the Kerr theorem) and
analyze the corresponding "particle-like" field distributions, with bounded
singularities of the associated physical fields. These can be obtained in a
straightforward algebraic way and exhibit non-trivial collective dynamics
simulating physical interactions
