Abstract | The bilinear approximation of force-deformation capacity curves is investigated for structural systems with non-negative-stiffness. This piecewise linear approximation process factually links capacity and demand; it lies at the core of the nonlinear static assessment procedures, and it has become part of seismic guidelines and codes, such as ASCE-41 and Eurocode 8. Despite codification, the various fitting rules, used to derive the bilinear representation, can produce highly heterogeneous results for the same capacity curve. This is especially valid for highly-curved backbones resulting from structural models with accurate representation of the initial, uncracked, stiffness or buildings characterized by a global collapse mechanism that leads to a gradual plasticization of the elements. The error introduced by the bilinearization of the force-deformation relationship is quantified by studying it at the single-degree-of-freedom (SDOF) level, away from any interference from multi-degree-of-freedom (MDOF) effects, thus avoiding the issue related to MDOF – SDOF approximation. Incremental Dynamic Analysis (IDA) is employed to enable a direct comparison of the actual backbones versus their bilinear approximations in terms of the spectral acceleration capacity for a continuum of limit-states, allowing a direct comparison of the results in terms of seismic performance. Code-based procedures are found to be less than ideal wherever there are significant stiffness changes, while in general remaining relatively conservative. The practical fitting rules determined allow, instead, a near-optimal fit regardless of the details of the capacity curve shape.