We study the interaction of the swift Ｃ60 ion-clusters with solids. The dynamic interacting forces acting on the individual ions in the cluster are derived based on the linear-response dielectric theory with the PLA dielectric function, and a set of equations describing the motion of the individual ions is obtained. It has been shown that by solving the equations of the motion, the wake effects of the dynamic interactions result in the strong asymmetric structures of the high-velocity C60 clusters, i.e., the leading ions in the cluster explode very fast, while the trailing ions in the cluster almost remain in stable states.