In an apparatus for positioning an optical element in a structure, particularly in an objective housing of a projection objective for microlithography, the optical element is connected to the structure via fastening elements. The position of the optical element is set by means of adjusting fasteners. The fastening elements are arranged in such a way and the adjusting fasteners can be actuated in such a way that the optical element can be tilted about three mutually independent axes and can additionally be displaced in a translatory fashion in one axial direction