This paper studies a dynamic game where each of two large blocs, of fossil fuel importers and exporters respectively, sets either taxes or quotas to exercise power in fossil-fuel markets. The main novel feature is the inclusion of a "fringe" of non- strategic (emerging and developing) countries which both consume and produce fossil fuels. Cumulated emissions over time from global fossil fuel consumption create climate damages which are considered by both the strategic importer and the non-strategic countries. Markov perfect equilibria are examined under the four combinations of trade policies and compared with the corresponding static games where climate damages are given (not stock-related). The main results are that taxes always dominate quota policies for both the strategic importer and exporter and that "fringe"countries bene?t from a tax policy as compared with a quota policy for the strategic importer, as the import fuel price then is lower, and the strategic importer's fuel consumption is also lower, thus causing fewer climate damages.