See also: Extraterritoriality. Extraterritorial jurisdiction (ETJ) is the legal ability of a government to exercise authority beyond its normal boundaries.Any authority can claim ETJ over any external territory they wish.However, for the claim to be effective in the external territory (except by the exercise of force), it must be agreed either with the legal authority in the external territory, or with a legal authority which covers both territories.he phrase may also refer to a country's laws extending beyond its boundaries in the sense that they may authorise the courts of that country to enforce their jurisdiction against parties appearing before them in respect of things that they did outside that country.