This paper uses a time-varying parameter model with generalized autoregressive conditional heteros-cedasticity effects to examine the dynamic behavior of crude-oil prices for the period 1997-2008. Using data from four countries of the Gulf Cooperation Council, we find evidence of short-term pre-dictability in oil-price changes over time, except for several short sub-periods. However, the hypothe-sis of convergence towards weak-form informational efficiency is rejected for all markets. In addition, we explore the possibility of structural breaks in the time-paths of the estimated predictability indices and detect only one breakpoint, for the oil markets in Qatar and United Arab Emirates. Our empirical results therefore call for new empirical research to further gauge the predictability characteristics and the determinants of oil-price changes.