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 an active control system, in addition to the semi-passive approach, is likely to give a substantial reduction in the lateral vibration level. The paper addresses some design aspects and different controller structures for the active control system. The adaptive controller is based either on feedforward or feedback control strategy. Results from computer simulations indicate that a feedback system would function as well as a multiple-reference feedforward system. However, by using a robust feedback-LMS controller the complexity of the control system may be reduced substantially. The control results illustrate an attenuation of the lateral train-car vibration by up to 15 dB.