Linear single-stage vibration isolation systems have a limitation on their performance, which can be overcome passively by using linear two-stage isolations systems. It has been demonstrated by several researchers that linear single-stage isolation systems can be improved upon by using nonlinear stiffness elements, especially for low-frequency vibrations. In this paper, an investigation is conducted into whether the same improvements can be made to a linear two-stage isolation system using the same methodology for both force and base excitation. The benefits of incorporating geometric stiffness nonlinearity in both upper and lower stages are studied. It is found that there are beneficial effects of using nonlinearity in the stiffness in both stages for both types of excitation. Further, it is found that this nonlinearity causes the transmissibility at the lower resonance frequency to bend to the right, but the transmissibility at the higher resonance frequency is not affected in the same way. Generally, it is found that a nonlinear two-stage system has superior isolation performance compared to that of a linear two-stage isolator.National Natural Science Foundation of ChinaHarbin Engn Univ, Power & Energy Engn Coll, Harbin 150001, Peoples R ChinaUniv Estadual Paulista UNESP, Dept Engn Mecan, BR-56153850 Ilha Solteira, SP, BrazilUniv Estadual Paulista UNESP, Dept Engn Mecan, BR-56153850 Ilha Solteira, SP, BrazilNational Natural Science Foundation of China51375103