Analytical probabilistic vulnerability analysis requires extensive computing effort as a result of the randomness in both input motion and response characteristics. In this study, a new methodology whereby a set of vulnerability curves are derived based on the fundamental response quantities of stiffness, strength and ductility is presented. A response database of coefficients describing lognormal vulnerability relationships is constructed by employing aclosed-form solution for a generalized single-degree-of-freedom system. Once the three fundamental quantities of a wide range of structural systems are defined, the vulnerability curves for various limit states can be derived without recourse to further simulation. Examples of application are given and demonstrate the extreme efficiency of the proposed approach in deriving vulnerability relationships.