We replicate the study of Tabak & Cajueiro (2007): "Are the crude oil markets becoming weakly efficient over time? A test for time-varying long-range dependence in prices and volatility" published in Energy Economics 29, pp. 28-36. The results have been mostly confirmed. Specifically, we have confirmed that the crude oil markets efficiency could be rejected up till approximately 1994 and this holds for both studied crude oil commodities - Brent and WTI. Analyzing an extended dataset up till June 2017, we find that the markets remained efficient (at least with respect to long-range dependence) until the outbreak of the Global Financial Crisis in 2008. This is confirmed by all three applied methods - the rescaled range analysis used in the original study, and the detrended fluctuation analysis and the Geweke-Porter-Hudak estimator which were added for stronger validity of the results. The markets returned back to efficiency around 2012 and remained there until 2015 when the Hurst exponent started another rally and stayed rather high until the end of the examined sample. Comparing the two markets, the Brent crude oil shows stronger signs of inefficiency during the inefficient periods compared to the WTI crude oil. This is in hand with the results reported in the original study. Apart from rerunning the analysis on an extended dataset and using two additional methods, we also provide a firmer validity check using the movingblock bootstrap procedure, which outperforms the original shuffling procedure in the provided forecasting study.