  We study infinite approximate subgroups of soluble Lie groups. Generalising a
theorem of Fried and Goldman we show that approximate subgroups are close, in a
sense to be defined, to genuine connected subgroups. Building up on this result
we prove a structure theorem for approximate lattices in soluble Lie groups.
This extends to soluble Lie groups a theorem about quasi-crystals due to Yves
Meyer.
