In this paper a new control technique based on the LAC/HAC concept is proposed to suppress the vibration of flexible space structures. The new technique employs the mechanism to turn on or off the HAC part of the LAC/HAC system in such a manner as to suppress the spillover effects as quickly as possible. The control system designed by the new technique has global stability and is more effective than a pure LAC system, even when an ordinary LAC/HAC system results in failure because of spillover instability. To show the characteristic features of the new technique and how to implement the system, computer simulation examples are given. Finally, the technique is applied to the transversal vibration control of a cantilever beam to show its effectiveness and practicality.