  It is shown that elementary excitations in fractal media obey the so-called
parastatistics of a variable order. We show that the order of the
parastatistics $N(k) $ is a function of wave numbers $k$ which depends on the
fractal dimension $D$ as $N(k) \sim k^{D-3}$ and represents a specific
characteristic of such media. This function $N(k)$ defines properties of the
ground state for excitations and the behavior of the spectrum of thermal
fluctuations. In particular, in fractal media fluctuations of the density
acquire an amplification by the factor $N(\omega) \sim \omega ^{D-3}$ which can
be related to the origin of $1/f$-noise.
