This article states the basic peculiarities of the behavior of the debt crisis in the Eurozone, and defines basic areas of overcoming this crisis. Based on the materials stated in this article, we made the following principal conclusions: The European Union is the most powerful and important economic and political union of states that plays the leading role in the global politics and world economy. The Eurozone formed in the European Union (economic currency union) consists of the strongest and rather weak economies. It affects the financial and economic state of the Eurozone (Euro-19), as well as the efficiency of managing state debt obligations. Further expansion of the European Union is characterized by the limiting factors, including by reason of the incompletion of institutionalization and integration processes in this economic and political union of countries. It creates new financial risks and potentiates the development of the debt problem. Solving the debt problem of the Eurozone has two variants (soft and tough models). The use of the tough model may finally cause the formation of the federative state (integration strengthening). It will affect national, economic, and political component of the European Union development. The use of the soft model can cause the disintegration, i.e. it will stipulate the exit of the economically weakest European countries from the zone. It will affect the reputation of the European Union and its positions in the world economy. Probably, in order to solve the debt problem, a complex of solutions will be used. It includes separate components of the soft and the tough models. It will also mean the transfer to a new institutional formation of the European Union, as well as legal basics of the economic and political union of European countries