Islam is a phenomenon which is present and increasingly conspicuous in EU Member States in social, political and also legal dimensions. The positive picture of the relations between the societies – hosts and Muslims is, however, interfered in such dimensions.The present author seeks what has caused this state of affairs, as well as attempts to formulate a recipe for a practical coexistence of the Western-Christian and Enlightenment concept of freedom and individual rights with the Islamic concept of individual rights. By defining Islam’s attitude to human rights and indicating the limited compatibility of both concepts of individual rights, the present author discerns the factors of their convergence in the process of secularisation of the Islamic concept of human rights and in the rise of the level of self-organisation of Muslim communities. The signpost in this process is to be the European Convention on Human Rights and the jurisprudence of the European Court of Human Rights. What offers a chance for the convergence of both concepts of human rights: Western and Islamic is the concept of Euroislam.