  In this paper we study the existence of higher dimensional arithmetic
progression in Meyer sets. We show that the case when the ratios are linearly
dependent over $\ZZ$ is trivial, and focus on arithmetic progressions for which
the ratios are linearly independent. Given a Meyer set $\Lambda$ and a fully
Euclidean model set $\oplam(W)$ with the property that finitely many translates
of $\oplam(W)$ cover $\Lambda$, we prove that we can find higher dimensional
arithmetic progressions of arbitrary length with $k$ linearly independent
ratios in $\Lambda$ if and only if $k$ is at most the rank of the $\ZZ$-module
generated by $\oplam(W)$. We use this result to characterize the Meyer sets
which are subsets of fully Euclidean model sets.
