Traditionally, control algorithms for Terfenol-D® magnetostrictive actuators have modelled the strain as a linear function of magnetic field and stress, but nonlinearity becomes important for strains of more than a few hundred parts per million (ppm), and for many applications even the maximum strain, about 1500 ppm, is inadequate. Larger strokes can be obtained by various types of stroke amplifiers, by resonant operation, or by inchworming. Previously, SatCon successfully used a 10:1 lever arm stroke amplifier in a helicopter flap actuator . Current projects include a water pump using a hydraulic stroke amplifier, which potentially could be more compact and efficient than a lever arm amplifier, and linear and rotary inchworm motors for robotics. In all these designs, satisfactory performance requires careful attention to machining tolerances and to making the mechanisms and housing stiff enough or compliant enough. A model for inchworm motors has been developed, including finite load and resonant effects. Nonlinear control algorithms will be discussed, applicable to arbitrarily large Terfenol-D® strains, stresses, and magnetic fields.