  We show that uniform approximate lattices in nilpotent Lie groups are subsets
of model sets. This extends a theorem due to Yves Meyer about quasicrystals in
Euclidean spaces. To do so we study relatively dense subsets of simply
connected nilpotent Lie groups and their logarithms. We then deduce a simple
criterion for the existence of an approximate lattice in a given nilpotent Lie
group.
