An apparatus for the precision positioning of an optical component a group of lenses or mirror, in the axial direction and/or for tilting the component and has an axial adjustment device and/or a tilting device. The axial adjustment device has an adjusting nut that includes a guide ring and a clamping ring. The two rings are connected to one another elastically via a blade. Individual clamping jaws are formed by axial incisions in the clamping ring and are braced with the guide ring via tensioning members. The tilting device has an inner and an outer tilting part. The inner tilting part is connected to the outer tilting part via torsion joints, and the outer tilting part is connected to a bearing part via torsion joints.