The paper introduces a novel approach for modeling nonlinear hysteretic behavior of reinforced concrete structures in the complex frequency domain. The new approach can be used to perform fast and accurate nonlinear SSI analyses, including sophisticated nonlinear hysteretic models, at a small fraction of the runtime of a time domain nonlinear SSI analysis. A case study of a typical low-rise shearwall nuclear plant structure is shown to demonstrate the proposed nonlinear SSI analysis approach. The story drifts, shear forces and in-structure acceleration response spectra (ARS) computed using both linear elastic and nonlinear SSI analyses are compared for the design level earthquake input with 0.30g ZPGA and a severe review level earthquake input with 0.70g ZPGA. The new nonlinear SSI approach also eliminates the need to use simplified cascaded multistep approaches that loose physics by neglecting the effects of the structural degradation on the SSI system dynamic behavior.