For the design of shell-like space frames located in seismic area, it is very important to give considerable attention to the dynamic behavior and to make clear how to reduce the seismic response. For the difficult dynamic problem of single layer latticed cylindrical roof structures, this study has previously analyzed their fundamental earthquake response behavior using the finite element method, and showed the relationship between the strain energy and the various response quantities in detail. This paper shows the earthquake response behavior of those with hysteresis dampers in the substructure and suggests the usefulness of this new structural control system.