Abstract: A magnetically levitated vibration damping apparatus includes a table having a flat board of a magnetic material, an electromagnetic actuator for applying magnetic attractive forces to the flat board to levitate the table, a displacement sensor for detecting relative displacement between the flat board and the electromagnetic actuator, an acceleration sensor for detecting absolute acceleration of the table, and a control system for controlling a current supplied to the electromagnetic actuator based on signals from the displacement sensor and the acceleration sensor according to a first control rule for controlling a gap between the flat board and the electromagnetic actuator based on the signal from the acceleration sensor and a second control rule for controlling vibrations of the table based on the signal from the acceleration sensor, the second control rule including stability control of relative displacement of the table.