A number of academics, journalists and political elites claim that Irish neutrality is a 'myth', and many also characterise public support for Irish neutrality as 'confused' and 'nonrational'. This 'unneutral' discourse in the academic literature and mainstream Irish media is based on an academic thesis, that of an Unneutral Ireland. The Unneutral thesis constructs a particular concept of neutrality in order to draw its conclusion that Ireland is 'unneutral'. Using a poststructuralist approach--a rarity in the discipline of International Relations (IR)--this paper deconstructs concepts of Irish neutrality using a framework of IR theories. The results show that the concept of neutrality put forward in the Unneutral Ireland thesis and the dominant discourses on Irish neutrality are based on a hegemonic IR theory, the theory of neorealism, rather than on seemingly 'objective' scientific research methods. The paper concludes that non-realist theories and approaches may provide a better understanding of Irish neutrality and of the dynamics of public support for Irish neutrality.