The characterization of strength of earthquake demands for seismic analysis or design requires the specification of a level of intensity. Numerous ground motion intensity indices that have been proposed over the years are being used for normalizing or scaling earthquake records regardless of their efficiency. An essential point of this study is that a ground motion index is appropriate, or efficient, as long as it can predict the level of structural response. This study presents correlations between 23 ground motion intensity indices and four response variables: elastic and inelastic deformation demands, and input energy and hysteretic energy; nonlinear responses are computed using elastoplastic, bilinear, and bilinear with stiffness degradation models. As expected, no index is found to be satisfactory over the entire frequency range. Indeed, indices related to ground acceleration rank better in the acceleration‐sensitive region of the spectrum; indices based on ground velocity are better in the velocity‐sensitive region and, correspondingly, generally occur in the displacement‐controlled region. Despite frequent criticism, the peak ground motion parameters passed the test successfully. A ranking of indices is presented, thus providing a choice of the most appropriate one for a particular application in the frequency range of interest.