The ‘strength’ of an earthquake ground motion is often quantified by an Intensity Measure (IM), such as peak ground acceleration or spectral acceleration at a given period. This IM is used to predict the response of a structure. In this paper an intensity measure consisting of two parameters, spectral acceleration and epsilon, is considered. The IM is termed a vector-valued IM, as opposed to the single parameter, or scalar, IMs that are traditionally used. Epsilon (defined as a measure of the difference between the spectral acceleration of a record and the mean of a ground motion prediction equation at the given period) is found to have significant ability to predict structural response. It is shown that epsilon is an indicator of spectral shape, explaining why it is related to structural response. By incorporating this vector-valued IM with a vector-valued ground motion hazard, we can predict the mean annual frequency of exceeding a given value of maximum interstory drift ratio, or other such response measure. It is shown that neglecting the effect of epsilon when computing this drift hazard curve leads to conservative estimates of the response of the structure. These observations should perhaps affect record selection in the future. Copyright © 2005 John Wiley & Sons, Ltd.