ABSTRACTThe shape of a uniform hazard spectrum has been criticized to be unrealistic for a site where the spectral ordinates of the uniform hazard spectrum at different periods are governed by different scenario events and conservative for long‐return‐period earthquake shaking. The conditional mean spectrum considering epsilon (CMS‐ε) takes into account the correlation of spectral demands (represented by values of ε) at different periods, to address these issues. This paper proposes new prediction models for the correlation coefficient of ε(T1) and ε(T2), a key component for developing a CMS, using Pan‐European earthquake records from a European ground motion database. Epsilon (ε) for each record is computed using the 2005 Ambraseys ground‐motion prediction equation. The model can be used to develop CMS for European sites, and it can be incorporated in the European seismic standards. Copyright © 2012 John Wiley & Sons, Ltd.