  We study the proximity effect of a superconductor to a normal system with
fractal spectrum. We find that there is no gap in the excitation spectrum, even
in the case where the underlying classical dynamics of the normal system is
chaotic. An analytical expression for the distribution of the smallest
excitation eigenvalue $E_g$ of the hybrid structure is obtained.On small scales
it decays algebraically as ${\cal P}(E_g)\sim E_g ^{-D_0}$, where $D_0$ is the
fractal dimension of the spectrum of the normal system. Our theoretical
predictions are verified by numerical calculations performed for various
models.
