A new control strategy which combines tuned mass damping (TMD) with base isolation (BI) concept is discussed in this paper by summarizing the working properties of the dual control strategy. To visualize the relationships between dynamic variables and subsystems, block-diagram illustrations are used which provide a mechanical view of this control strategy. It is shown that the BI technique applies an open-loop control law and that TMD uses a closed-loop control law. Seismic performances of combined systems are summarized showing numerical response tests of models subject to some recorded seismic excitations in linear and non-linear range and to stationary Gaussian random processes. Control effectiveness of TMD in reducing seismic vibrations of base isolated systems is compared with that produced by adding damping in the isolation layer.