  Using a real-space renormalization-group approximation, we study the
anisotropic quantum Heisenberg model on hierarchical lattices, with
interactions following aperiodic sequences. Three different sequences are
considered, with relevant and irrelevant fluctuations, according to the
Luck-Harris criterion. The phase diagram is discussed as a function of the
anisotropy parameter $\Delta$ (such that $\Delta=0$ and $\Delta=1$ correspond
to the isotropic Heisenberg and Ising models, respectively). We find three
different types of phase diagrams, with general characteristics: the isotropic
Heisenberg plane is always an invariant one (as expected by symmetry arguments)
and the critical behavior of the anisotropic Heisenberg model is governed by
fixed points on the Ising-model plane. Our results for the isotropic Heisenberg
model show that the relevance or irrelevance of aperiodic models, when compared
to their uniform counterpart, is as predicted by the Harris-Luck criterion. A
low-temperature renormalization-group procedure was applied to the
\textit{classical} isotropic Heisenberg model in two-dimensional hierarchical
lattices: the relevance criterion is obtained, again in accordance with the
Harris-Luck criterion.
