The right of pursuit belongs among the recognised exceptions to the principle of the exclusive jurisdiction of the state flag on the high seas. The development of the right of pursuit was part of an attempt to secure the effective protection of the interests of coastal states outside their own jurisdictions. The author discusses the right of pursuit, taking into consideration the decisions of the United Nations Convention on the Law of the Sea from 1982. The decision as to whether the reasons for undertaking pursuit are genuinely well-founded belongs, by the nature of things, to the coastal state. The right of pursuit can only be implemented by naval vessels or military aircraft, or by other sea vessels or aircraft clearly marked and readily identifiable as being in government service and entitled to undertake pursuit. Polish legislation relating to the right of pursuit is in accordance with the international legal norms that apply to this matter. In particular, this applies to the legislation's accordance with the decisions of the U.N. Convention on the Law of the Sea (1982), which was ratified by Poland in 1988.