Abstract A structure designed in a dual-system configuration can help to achieve a damage-control and an earthquake-resilient property. In a dual-system, the primary structural system (PSS) and the replaceable fuse act in parallel, and the entire structure exhibits a multi-stage yielding mechanism under earthquake actions. To ensure the PSS keeps elastic, the dual-system is required to have a sufficient first-yielding stage wherein the fuse yields to dissipate the input energy. Accordingly, prediction of the structural ductility demand (μ) associated with the first-yielding stage is an important issue. In the first-yielding stage, the PSS remains elastic, making the post-yield stiffness ratio (α) much larger than conventional structures. This paper focuses on the ductility demand of bilinear hysteretic systems embedded with the high-α characteristic, which represent the dual-systems behaving within the elastic and the first-yielding stages. A total number of 742 strong earthquake records (490 of them are from stiff soil according to the standard of ASCE/SEI 7-10) are adopted to compute the ductility demand of 19,200 bilinear single-degree-of-freedom hysteretic systems. These systems have different combinations of strength levels (strength reduction factor 1.25 ≤ R ≤ 5.00), post-yield stiffness ratios (0.05 ≤ α ≤ 0.80) and natural periods (0.05 s ≤ T ≤ 5.00 s). It is revealed that for α ≥ 0.30, a larger α would lead to a slightly increased μ. Therefore, improving the value of α would not alleviate the expected inelastic displacement demand associated with the first-yielding stage for a dual-system, even though a larger α could remarkably reduce the dispersion of μ. A probabilistic spectral model for μ is developed, based on which the seismic performance of a dual-system could be checked in a statistic way. A trial-and-error design process for dual-systems is given, and the design-check process of a five-story buckling-restrained-braced frame is illustrated using the spectral model of μ. This study provides instructive results for the seismic design and retrofitting of dual-systems, as the effects of α, R and T on the values of μ for dual-systems are quantified appropriately.