A procedure to account for the uncertainty in the characteristics of future ground motions during seismic response assessment is presented. In the proposed procedure, the probability of exceedance of structural response parameters conditioned to a given ground motion intensity is computed from a series of deterministic response history analyses at three loading intensity levels. The proposed procedure explicitly takes into account the variation of dispersion of the structural response with changes in the loading intensity. Regression analyses are conducted on the parameters of the conditional probability distribution in order to estimate the conditional probability of exceedance at other ground motion intensity levels. Results are then combined with probabilistic estimates of seismic loading in order to estimate the mean annual rates of exceedance of various structural response parameters. The proposed procedure is evaluated when applied to an existing seven-story reinforced concrete building. Results are also compared to those obtained with an existing simplified procedure. The effect of various simplifying assumptions made in the existing simplified solution are also evaluated. It is shown that neglecting variations in dispersion in some cases can lead to significant errors. It is concluded that the proposed procedure provides more accurate results than the simplified approach with only a minimum additional computational effort.