The European Union (EU) aims at increasing the competitiveness in EU markets via single prices for each commodity and service. Energy products are the basic necessary commodities for both production and consumption. This article examines light fuel oil and automotive diesel prices in some EU countries, among other energy prices, to reveal if traditional EU oil and diesel prices move towards an equilibrium single price. Employing panel data sets for industry oil price, household oil price, industry diesel price and household diesel price, this study reveals convergence in prices for panels through Lagrange Multiplier unit root tests with structural breaks. On the other hand, it also observed non-convergence for some individual EU members from the related panels. The speed of adjustment is another important issue together with convergence by itself. To this end, this work observes the half-lives of deviations of prices from their equilibrium levels as well and concludes that oil prices converge faster than diesel prices do.