The alignment device (10) is used for aligning an optical transmitting beam with an optical receiving beam. It comprises a rough alignment device and a fine alignment device. The rough alignment device has a first mirror (30.1), which can be rotated by approximately 360.degree. around a first axis (14), in respect to which the first mirror (30.1) is set at 45.degree. to the first axis. The rough alignment device furthermore has a second mirror (32.1), which can be rotated by approximately 180.degree. around a second axis (16), in respect to which the second mirror (32.1) is set at 45.degree.to the second axis. The second axis (16) can be rotated around the first axis (14), so that the second mirror (32.1) can be rotated within a spatial angle of approximately one hemisphere by the cumulative rotations around the axes (14, 16). The fine alignment device is constituted by a tiltable seating device (30.6 to 30.17) for at least one mirror (30.1), by means of which this mirror (30.1) is tiltably seated. The fine alignment device furthermore has an actuator device (30.18 to 30.19), by means of which the mirror (30.1) can be tilted in relation to its center normal line (15) within a spatial angle, which is considerably less than the hemisphere. At least the tiltably fastened one of the two mirrors (30.1, 32.1) is embodied with reduced mass.