SUMMARYA control strategy is proposed for variable damping elements (VDEs) used together with auxiliary sti!ness elements (ASEs) that compose a time-varying non-linear Maxwell (NMW) element, considering near-future excitation in#uence. The strategy "rst composes a state equation for the structural dynamics and the mechanical balance in the NMW elements. Next, it establishes a cost function for estimating future responses by the weighted quadratic norms of the state vector, the controlled force and the VDEs' damping coe$cients. Then, the Euler equations for the optimum values are introduced, and also approximated by the "rst-order terms under the autoregressive (AR) model of excitation information. Thus, at each moment t I , the strategy conducts the following steps: (1) identify the obtained seismic excitation information to an AR model, and convert it to a state equation; and (2) determine VDEs' damping coe$cients under the initial conditions at t I and the "nal state at t I>* , using the "rst-order approximation of the Euler equations. The control e!ects are examined by numerical experiments.