An inventive blood pump in accordance with this invention includes a housing that has inlet and outlet ports for receiving and discharging blood. A rotor is positioned in the housing's interior for pumping blood between the housing's inlet and outlet ports, with the rotor being capable of motion in three translational and three rotational axes. An assembly for magnetically suspending and rotating the rotor in a contact-free manner with respect to the housing includes only one electromagnetic bearing that actively controls motion of the rotor with respect to one axis selected from the rotor's three translational and three rotational axes, an electromagnetic motor that actively drives motion of the rotor with respect to one of its three rotational axes, and magnetic bearings for passively controlling motion of the rotor with respect to the remaining four of its translational and rotational axes. The inventive blood pump can also be incorporated into an artificial heart.