The problem of low-frequency lateral train-car vibration is an important issue surrounding the design of high-speed trains. Passive solutions such as stiffening the car chassis are impractical because of the weight increase. Semi-passive solutions, such as modifying the structural dynamics of the carbody through non-rigid coupling of heavy underfloor equipment does not incur a weight penalty, but does not sufficiently reduce the vibrations. However, computer simulations based on signals derived from a dynamic computer model of a train car indicates that the incorporation of a multiple-reference feedforward active control system, in addition to the semi-passive approach, is likely to effect a substantial reduction in the lateral vibration level. The complexity of the control system may be reduced by using a robust feedback-LMS controller. Results from computer simulations indicate that a feedback system would function as well as, and potentially better than, a feedforward system. The control results illustrate attenuation of the lateral train-car vibration of up to 15 dB.