For developed countries, the salient post-World War II economic experience is surely the long run growth of gross domestic product (GDP). The theoretical explanation for this empirical fact was offered by the neo-classical theory of economic growth, which established that in equilibrium, the economy grows with constant rates for various variables. This situation is called steady-state growth, and is determined by certain structural parameters of the economy. Economies with similar tastes and production technologies have the same steadystate. If these economies differ in the initial quantity of capital per person, the theory implies that the less advanced of them have a higher growth rate than the other. This transition hypothesis is referred to as absolute β-convergence. If the steady-states differ, then an economy grows faster the further it is from its own steady-state value. This situation is referred to as conditional β- convergence. A third type of convergence (σ-convergence) occurs if the dispersion measured by the standard deviation of the logarithm of per capita income across several economies declines over time. Finally, we find stochastic convergence if the time series of per capita GDP differences between two countries, or a country and an average per capita GDP of a group of countries is stationary. The empirical results presented in this paper all offer strong support for the presence of convergence among the EU 15 Countries.