International human rights law imposes obligations on States that have jurisdiction over facts occurring in the ‘grey zone’, namely, the territorial State and the outside State. The principal question which the chapter answers is dual: what the scope of the obligations binding the concerned States is in respect of the ‘grey zone’ and what the limits are of these obligations, especially compared to the obligations binding them in a ‘normal’ situation where the State has effective control over its entire territory. The chapter claims that the degree of the State’s effectiveness and the lawful limitations the State introduces can decrease the modalities of the expected protection but cannot restrict the heart of the obligations under human rights conventions.