  The indefinite Sturm-Liouville operator $A = (\sgn x)(-d^2/dx^2+q(x))$ is
studied. It is proved that similarity of $A$ to a selfadjoint operator is
equivalent to integral estimates of Cauchy integrals. Also similarity
conditions in terms of Weyl functions are given. For operators with a
finite-zone potential, the components $\Aess$ and $\Adisc$ of $A$ corresponding
to essential and discrete spectrums, respectively, are considered. A criterion
of similarity of $\Aess$ to a selfadjoint operator is given in terms of Weyl
functions for the Sturm-Liouville operator $-d^2/dx^2+q(x)$ with a finite-zone
potential $q$. Jordan structure of the operator $\Adisc$ is described. We
present an example of the operator $A = (\sgn x)(-d^2/dx^2+q(x))$ such that $A$
is nondefinitizable and $A$ is similar to a normal operator.
