  We consider the Schwarzschild black hole and show how, in a theory with
limiting curvature, the physical singularity "inside it" is removed. The
resulting spacetime is geodesically complete. The internal structure of this
nonsingular black hole is analogus to Russian nesting dolls. Namely, after
falling into the black hole of radius $r_{g}$, an observer, instead of being
destroyed at the singularity, gets for a short time into the region with
limiting curvature. After that he re-emerges in the near horizon region of a
spacetime described by the Schwarzschild metric of a gravitational radius
proportional to $r_{g}^{1/3}$. In the next cycle, after passing the limiting
curvature, the observer finds himself within a black hole of even smaller
radius proportional to $r_{g}^{1/9}$, and so on. Finally after few cycles he
will end up in the spacetime where he remains forever at limiting curvature.
