An immersion lithography objective has a housing in which at least one first optical element is arranged, a second optical element, which follows the first optical element in the direction of the optical axis of the objective, an immersion medium that adjoins the second optical element being located downstream of the latter in the direction of the optical axis, and a retaining structure for the second optical element. The retaining structure has a greater stiffness in the direction of the optical axis than in a direction perpendicular to the optical axis.