The stochastic and β convergences of per capita energy use (PCEU) in the OPEC member countries are examined during the period 1971-2011. Several unit root tests, including the test introduced by Lee and Strazicich (2003) are used to examine the existence of the stochastic convergence in the series. Next, to study the possibility of the existence of β-convergence, the approach of Perron and Yabu (2009) is employed. Both methods allow for an endogenous structural break point in the series. In addition, the approach of Perron and Yabu (2009) is robust to the presence of a unit root and the results remain the same for the unit-root and stationary series. The results show that the PCEU in Angola, Ecuador, Iran, Nigeria, Qatar, and Venezuela had experienced beta convergence during the first regime (the period before the break point). In the second regime, the PCEU in Algeria, Angola, Saudi Arabia, Ecuador, UAE, Iran, Iraq, Libya, and Qatar shows a convergent pattern. In addition, the estimated break points are clustered and correspond to the major energy and economic crises.