The dynamic behaviour of benchmark highway bridges using variable dampers under six bidirectional earthquake ground motions is presented. A viscous damper is used as a passive control device and a variable damper, developed from an MR (magnetorheological) damper, is used as a semi-active control device. The study is based on the simplified lumped-mass finite-element model of the 91/5 highway bridge in Southern California. The prime aim of the study is to investigate the effectiveness of viscous dampers and variable dampers with a friction-type damping force scheme and a two-step viscous damping force scheme, with important parametric variation. Velocity-and displacement-dependent models of a variable damper are used. Numerical simulations are conducted by installing the devices between the deck and abutments of the bridge. The seismic response of the bridge is compared with the corresponding uncontrolled case, and controlled by alternative sample control strategies. The results of the investigation clearly indicate that the base shear and mid-span displacement are reduced substantially by these protective devices. It is concluded that variable dampers are quite effective in considerably reducing the large bearing displacements, thereby eliminating the isolator damages. The control effect of a viscous damper, and the two pre-set damping schemes of a variable damper in particular, is quite satisfactory in reducing the peak response quantities of the bridge to a level comparable to or better than that of the sample passive, semi-active and active controllers.