Introduction. Terrorism as a socio-political phenomenon that violates the security, rights and interests of the individual, society and the state, puts forward new tasks for constitutional construction in a globalizing world. That is why the article examines the current constitutional and legal models of countering terrorism. The author analyzes various points of view of scientists and politicians on the relationship of human rights, as well as other constitutional values with measures of response to an emergency. Theoretical analysis. The study of the constitutional and legal models of countering terrorism is important not only from a theoretical, but also from a practical point of view, since the most serious and systematic abuse of exclusive powers and violations of human rights occur during countering threats to public order and national security. Empirical analysis. Considering the models for the application of exceptional measures in emergency situations, we draw attention to the following important factors within the framework in which they are implemented: whether the exceptional anti-terrorist measures are aimed at protecting the constitutional order, human rights and freedoms or when they are introduced, other goal-setting is possible; whether the state considers anti-terrorist measures to be extraordinary or proceeds from the assumption that their use is possible in the normal course of the exercise of state power; whether the transition of the state from emergency measures to the usual regime of exercising state power has been ensured in a normative way. Results. Systematizing the views of scientists on the problem of state countering terrorism, we have identified the following basic constitutional and legal models: the absolutization of human rights, non-constitutional and based on achieving a balance of public and private interests.