An illumination system of a microlithographic exposure apparatus has an optical axis and a beam transforming device. This device includes a first mirror with a first reflective surface having a shape that is defined by rotating a straight line, which is inclined with respect to the optical axis, around the optical axis. The device further includes a second mirror with a second reflective surface having a shape that is defined by rotating a curved line around the optical axis. At least one of the mirrors has a central aperture containing the optical axis. This device may form a zoom-collimator for an EUV illumination system that transforms a diverging light bundle into a collimated light bundle of variable shape and/or diameter.