A squeeze film damper is a device for passive vibration control of rotors. An adaptive squeeze film damper is one whose properties can be continuously adapted to minimize the amplitude of vibration of the rotor in any working condition. This paper concerns an adaptive squeeze film damper with a magneto-rheological fluid (MR): a change of its apparent viscosity is obtained by applying a magnetic field through the fluid and hence the damping effect of the device can be varied. The emphasis is placed on the control algorithm for the real-time adaptation of the device. Firstly, a fuzzy control that applies empirical rules, designed by the authors, is used. The inputs of the controller are the rate of change in the amplitude of vibration, the amplitude of vibration and the rate of change of the control output, which is the current supplied to the coils generating the magnetic field. An optimization of the controller rules is then obtained using genetic algorithms.