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The resonant-column test is widely used for dynamic characterization of soils under different confinement and shear-strain conditions. The free-decay response of a soil specimen in resonant-column testing shows a nonlinear behavior when the strain levels exceed a threshold shear strain. However, the dynamic parameters are commonly determined assuming a linear single-degree-of-freedom (SDOF) model. This paper presents a new analysis methodology based on the complex exponential method (CEM) for the nonlinear dynamic characterization of soil specimens using the free-decay response in torsional fixed-free resonant-column testing. This analysis methodology represents a solution to the chronic problem of evaluating the dynamic properties of soils while avoiding the negative effects of imposing many loading cycles at strain levels greater than the threshold shear strain, which, in turn, change the original dynamic properties of soil specimens. The effectiveness of the proposed analysis methodology is demonstrated on a dry-sand specimen tested under isotropic loading and unloading conditions, two confining pressures (40 and 100 kPa), and different shear-strain levels (1. 34 X 10-5 ≤ γ ≤1. 52 X 10-3). The results from the CEM are compared with the results from traditional linear SDOF methods (transfer function and free-decay response). Damping ratios obtained from the CEM are also compared with values obtained using the empirical-mode-decomposition-Hilbert-transform (EMD-HT) method. The results show that the damping ratio can be underestimated up to 80% at strain levels greater than the threshold shear strain when computed using linear SDOF models. In a nonlinear free-decay response in resonant-column testing analyzed using the CEM, it is possible to observe that the dry-sand specimen becomes denser (stiffer). Thus the shear-wave velocity (resonant frequency) increases at the low shear-strain levels imposed during the same test. [ABSTRACT FROM AUTHOR]