In a bending machine for bending rod-shaped workpieces made from wire, tubular material or the like, a machine frame is provided with at least one bending station comprising two bending units. Each of said bending units comprises a bending head with a bending head housing and a bending tool, an auxiliary gripper arranged on the bending head housing so as to be pivotable perpendicular to the longitudinal axis of the machine frame, and a gripping unit, which is spaced apart from the bending head as viewed along the longitudinal axis of the frame, pivotable perpendicular to the longitudinal axis of the machine frame and displaceable on a guide in the direction of said axis. The two bending heads of each bending station are arranged next to each other with their auxiliary grippers facing each other and are positioned between the two gripping units such that each bending head—viewed in the direction of the frame's longitudinal axis—is mounted between the other bending head and the gripping unit associated with the other bending head.