This paper investigates the relationship between energy intensity in the 12 countries of Eastern Europe that can be considered as in transition to a full market economy, and that of the present EU members. The raw data shows some evidence of convergence, and a carefully estimated econometric model of lagged adjustment confirms this. On average, a 1% decrease in the per capita income gap between developed and transition economies leads to a decrease in the energy intensity growth rate of a transition country by 0.7%. There are differences in the rate of convergence across countries, and these depend on two parameters that are allowed to vary across countries: ç, the elasticity of desired energy intensity with respect to the per capita income gap; and µ, the rate at which actual energy intensity adjusts to the desired energy intensity. The countries with the fastest convergence rates given these parameters are the Czech Republic, Bulgaria, Croatia and Turkey. The forecast values for energy intensity and actual energy demand levels of seven transition countries were estimated. Results show that the energy intensities of transition countries except Estonia converge to EU levels significantly. On the other hand, actual energy demand levels between 2000 and 2020 show an increasing demand in all 7 countries despite the reductions in energy intensity. Therefore, it will not be feasible to use as a target a non-increasing level of total energy consumption.