We have studied the structural properties of single and multiple layers of self-organised Ge islands grown on Si. The X-ray reflection curves of the single layers indicate the transition from 2D to 3D growth for Ge layer thicknesses of 5.33–5.67 ML, in excellent agreement with photoluminescence observations. Because of the strain fields extending into the surrounding Si barrier, the dots of multiple layers are strongly correlated in the vertical direction. A recent theoretical model also predicts an increasing lateral correlation of the dots with increasing numbers of dot layers. In reciprocal space maps we not only observed such a kind of lateral ordering, but also indications for an anisotropy of the inter-dot spacing in the  and  directions.