An active stabilizing device for a primary damping of rolling movements of a ship or other watercraft includes at least one positioning device including a drive journal and a stabilizing fin having a stabilizing surface and a root, the drive journal being attached to the stabilizing fin at the root, the stabilizing surface having a leading edge and a trailing edge and being configured to be disposed underwater. The positioning device is configured to simultaneously pivot the stabilizing fin about a pivot axis by a pivot angle and rotate the stabilizing fin about an axis of rotation. Also, a method of operating the active stabilizing device.