Before 2004 South Africa was the dominant steam coal exporter to the European market. However a new market situation with rising global demand and prices makes room for a new entrant: Russia. The hypothesis investigated in this paper is that the three incumbent dominant firms located in South Africa and Colombia reacted to that new situation by exerting market power and withheld quantities from the market in 2004 and 2005. Three market structure scenarios of oligopoly with a competitive fringe are developed to investigate this hypothesis: a Stackelberg model with a cartel, a Stackelberg model with a Cournot-oligopoly as leader and a Nash-bargaining model. The model with a Cournot oligopoly as leader delivers the best reproduction of the actual market situation meaning that the dominant players exert market power in a non-cooperative way without profit sharing. Furthermore some methodological clarifications regarding the modeling of markets with dominant players and a competitive fringe are made. In particular we show that the use of mixed aggregated conjectural variations can lead to outcomes that are inconsistent with the actions of rational profit-maximizing players.