  The earlier proposed conditions of (bi)quaternionic differentiability are
nonlinear, give rize to the 2-spinor and the self-dual gauge structures and may
be considered as the it generating system of equations (GSE) with respect to
the source-free Maxwell, Yang-Mills and eikonal equations. We present the
general solution of the GSE in terms of twistor variables, analize its rather
specific gauge symmetry and demonstrate the relation of GSE to the equations of
shear-free null congruences and, consequently, - to effective metrics of Kerr-
Shild type. The concept of particles as singularities of physical fields
associated with the solutions of GSE is developed
