Over the period 2015-2050 the consumption of natural gas of European OECD countries is expected to grow more than the consumption of any other energy source. Although these countries are interconnected and in most cases share a common currency, their wholesale national gas markets are highly heterogeneous. We study the determinants of cross-country convergence of natural gas prices for industrial consumers in fourteen European countries. Our empirical analysis is based on the notions of pairwise, relative and σ-convergence. We show that there is evidence of pairwise price convergence and that some key characteristics of gas markets, such as the maturity of trading hubs and the degree of interconnection, are positively associated with the existence of a convergence process. This result carries over to the notion of σ-convergence and is robust to a number of changes in the implementation of the statistical tests. The analysis of relative convergence points to the existence of price-growth convergence, while price-level convergence is not supported by the data. Lastly, we assess the the short-run implications of price convergence focusing on the speed of reversion to equilibrium after a system-wide shocks hits the cointegrating relation.