A multi-leaf collimator includes leaf drives and two sets of displaceable leaves arranged side by side and facing each other to impress a high-energy beam with the shape of an irregularly formed treatment object. Each of the leaves assumes a position oriented along the shape of the treatment object by means of a leaf drive and each are equipped with a gear rod-like drive engagement in the direction of the displacement. A leaf-side pivotable gear segment is located, together with a motor-side gear segment, on a segment disk that engages with the gear rod-like drive engagement. A pinion drivable by a motor engages with the motor-side gear segment. The segment discs are arranged side by side for each set of leaves as a package on one axis. The motor-side gear segments of two segment disks located next to each other are staggered so that they will not abut each other.