The article features the civil component of the crisis response in the European Union, as well as the Russian role in its development. With the new security threats and challenges, the civilian instruments necessary for the post-conflict society stabilization are becoming increasingly important. The research was based on the universal evolutionism and included such methods as conceptual and structural modeling, comparative analysis, and historical approach. The methods made it possible to reveal the civil component within the crisis management system of the European Union. The civil component unites and coordinates European national resources, creates platforms and opportunities for experience exchange, increases the motivation and professionalism of experts, etc. The author also focused on the interaction between the European Union and the Russian Federation in this sphere. The key parameters for developing the civil dimension of crisis response include two points: (1) the political will to implement the civilian component of security policy by the European Union institutions and member states, (2) the will to solve the problem of human resources. For the current and foreseeable Russian-European relations, the cooperation potential of the civilian component of crisis response is not included in the security policy. The research makes a significant contribution to the study of the European Union development problems, genesis and development parameters of the civil missions, and the Russian-European dialogue.