The peak deformation, acceleration, and the base shear experienced by the structures can be reduced by simulating yielding in an elastic system-also referred as apparent weakening. The negative stiffness device (NSD), used in this study, exhibits nonlinear-elastic negative stiffness behavior; by adding NSD to the elastic structure (primary structure), the resulting structure-device assembly behaves like a bilinear-elastic structure. In an elastic structure, the acceleration and base shear experienced by the structure can be reduced by adding the negative stiffness device, and the additional deformations caused from the reduced stiffness can be contained by adding viscous dampers. Previously, the authors have carried out experimental studies to demonstrate the effectiveness of apparent weakening in elastic structures, but little is known about the behavior of these systems when the primary structure itself yields. This paper focuses on the issues that may emanate with the addition of NSD to the systems prone to yielding while highlighting the response reduction achieved by proper design of the NSD. Shake-table studies of a three-story fixed-base structure (3SFS) braced in top two stories, that is acting as a single degree of freedom system (SDOF) are presented in this paper. Two NSDs and a viscous damper are installed in the first story of the SDOF-3SFS. The structure is subjected to strong ground motions, with and without the NSDs, so that the columns of the SDOF-3SFS in the first story yield. Analytical models for all the components, that can capture the observed experimental behavior, are also presented in this paper. To demonstrate the advantages of apparent-weakening in yielding SDOF structures, experimental and analytical responses of four different systems, (1) 3SFS, (2) 3SFS with damper, (3) 3SFS with NSD, and (4) 3SFS with NSD and damper, are compared for a suite of ground motions. Shake-table tests on SDOF-3SFS have confirmed that by adding the NSD and damper, the acceleration and base shear and deformation of the bilinear inelastic structure and NSD assembly will be reduced by more than 20% for moderate ground motions, and the collapse of structure can be prevented for severe ground motions. (C) 2014 American Society of Civil Engineers.