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 interdot spacing in the [100] and [110] directions.