Structural changes in the European natural gas market such as liberalization, increasing domestic demand, and increasing import dependency have triggered new attempts to model these markets accurately. In this paper, we propose an exhaustive model of the European natural gas supply including the possibility of strategic behaviour of the agents along the value-added chain. We structure it as a two-stage-game with natural gas exports to Europe (first stage) and wholesale trade within Europe (second stage). The case of non-cooperative Cournot competition at both stages proves to be the most realistic scenario. The results of the perfect competition and cartel scenario are also presented. Our results suggest that the main suppliers of natural gas to Europe (Russia, Algeria, the Netherlands, Norway) remain dominant, but that they are complemented by overseas supplies of liquefied natural gas (LNG). The model also enables us to identify transport infrastructure bottlenecks where transport capacity constraints are binding.