Digital transformation of European border management entails multiple benefits. Novel digital systems and cyber-physical infrastructures, such as biometrics-enabled automated border control and advanced analytics aim to equip border agencies with more effective tools against constantly evolving border security threats. Additionally, they provide new means to increase the agencies' performance in the context of growing volumes in trade and travel. Besides a myriad of opportunities for improved border management, the development, deployment and sophistication of these technologies compared to legacy systems bring about new vulnerabilities that may be hard to identify and manage with techniques used today. This paper employs a systems-theoretic approach to address the security of border control systems. The focus is on border checks, which involve technologies used for ensuring and controlling that persons and the objects in their possession are authorised to enter or exit the EU area at external borders. The paper provides a preliminary review of current literature and discusses the basic tenets and main features of security analyses in this field by reflecting them against the STAMP model and the STPA technique for security analysis purposes. The systems-theoretic approach is demonstrated in this paper by presenting the first phase of a coarse STPA-inspired security analysis at air borders with a particular interest on automated border control systems. Based on the analysis, STPA was found as a suitable approach for security analysis, as it supports assessment of the interactions between various stakeholders within the border control system. As a conclusion, we also provide insights for future research directions in cyber-physical border check systems and applications of systems-theoretic analysis methods in this particular field.