High-static-low-dynamic-stiffness (HSLDS) nonlinear isolators have proven to have an advantage over linear isolators, because HSLDS nonlinear isolators allow low-frequency vibration isolation without compromising the static stiffness. Previously, these isolators have generally been assumed to have linear viscous damping, degrading the performance of the isolator at high frequencies. An alternative is to use nonlinear damping, where the nonlinear behavior is achieved by configuring linear dampers so they are orthogonally aligned to the excitation direction. This report compares the performances of single-stage and two-stage isolators with this type of damping with the corresponding isolators containing only linear viscous damping. The results show that both isolators with linear viscous damping and nonlinear damping reduce the transmissibility around the resonance frequencies, but the results show that the isolators with nonlinear damping perform better at high frequencies.