According to core UN and Council of Europe human rights treaties each state party undertakes to respect and to ensure (or to secure) to all individuals within its territory and/or subject to its jurisdiction the rights (and freedoms) recognized in the treaties. Provisions of this kind suggest that the rights recognized in the treaties are rights of everyone everywhere. Nevertheless, there are certain well-known exceptions. The problem with these exceptions is a) that they are conceived as exceptions to ‘everyone’, although they are exceptions to “everywhere’, b) that they are not in fact exceptions but different kinds of rights and c) that many more, at least 16 rights are affected. In other words, this study shows that the rights recognized in the said instruments are divided into three groups: a) non-territorial rights (which everyone has everywhere in the world), b) territorial rights (which everyone has somewhere in the world) and c) territorially mixed rights (which everyone has partly everywhere and partly somewhere). This new classification is likely to contribute to a deeper and better understanding of human rights and human rights principles (in particular non-discrimination and equality) and to a more uncontroversial implementation of human rights treaties.