  We discuss basic features of the model of spinning particle based on the Kerr
solution. It contains a very nontrivial {\it real} stringy structure consisting
of the Kerr circular string and an axial stringy system.
  We consider also the complex and twistorial structures of the Kerr geometry
and show that there is a {\it complex} twistor-string built of the complex N=2
chiral string with a twistorial $(x,\theta)$ structure. By imbedding into the
real Minkowski $\bf M^4$, the N=2 supersymmetry is partially broken and string
acquires the open ends. Orientifolding this string, we identify the chiral and
antichiral structures. Target space of this string is equivalent to the
Witten's `diagonal' of the $\bf CP^3\times CP^{*3}.$
