Stiffening system is a system that its stiffness increases as it goes under large displacements. Such a behavioral characteristic often results from interaction due to gap closure between two parts of a system or between a primary system and its interacting environment (IE). Unlike softening systems, stiffening systems have not been studied. Several parameters are involved in defining a simple stiffening system. These parameters are; initial stiffness, yield force limit, gap size between primary system (herein Stiffening SDOF or S-SDOF) and its IE, the strength or yield force limit of the IE components, the stiffness of the IE components, and the mass ratio of the IE component to the primary system (S-SDOF). This paper presents results of a comprehensive parameter study considering over 367,000 cases. It is shown that the displacement and hysteretic energy response of SSDOF systems decreases by larger stiffness ratio and smaller gap size and smaller mass ratio. Variation of the strength ratio has negligible effect on the displacement response ratios. But S-SDOF systems dissipate higher hysteretic energy as strength ratio increases. Furthermore, in determining force and displacement responses of S-SDOF systems, the response modification factor and strength ratio are the most important parameters. Implications of these findings on development of design spectrum for stiffening systems are also discussed.