This paper investigates the effectiveness of various ground motion intensity measures (IMs) in estimating the structural response of two types of rocking systems: (a) a controlled rocking steel braced frame system with self-centering action and (b) a rocking spine system for reinforced concrete infill frames. The IMs are evaluated based on the dispersion in engineering demand parameter (EDP) predictions (efficiency) and the sensitivity of the conditional distributions of EDPs to the distributions of the magnitudes, distances and spectral shape parameter (ε) of ground motion records (sufficiency). The EDPs include maximum transient and residual story drifts and peak floor accelerations. The spectral acceleration averaged over a range of periods (Saavg) is most effective for predicting transient and residual drift demands and peak ground acceleration (PGA) is generally the best predictor of peak floor accelerations. The proximity of the frequency range most affecting an EDP to that best reflected in an IM is found to be a good indicator of the performance of that IM.