  We consider correlated L\'evy walks on a class of two- and three-dimensional
deterministic self-similar structures, with correlation between steps induced
by the geometrical distribution of regions, featuring different diffusion
properties. We introduce a geometric parameter $\alpha$, playing a role
analogous to the exponent characterizing the step-length distribution in random
systems. By a {\it single-long jump} approximation, we analytically determine
the long-time asymptotic behavior of the moments of the probability
distribution, as a function of $\alpha$ and of the dynamic exponent $z$
associated to the scaling length of the process. We show that our scaling
analysis also applies to experimentally relevant quantities such as escape-time
and transmission probabilities.
  Extensive numerical simulations corroborate our results which, in general,
are different from those pertaining to uncorrelated L\'evy-walks models.
