PurposeTo do this, the authors carried out a systematic literature review to answer three questions: (RQ1) Which external pressures affect an FC and its suppliers in an MSC? (RQ2) What influences power relationships between an FC and its suppliers for MSC compliance? and (RQ3) Which governance mechanisms support an FC to achieve compliance for managing its MSC?Design/methodology/approachThis research aims to identify how external pressures affect chain agents to achieve compliance and implement governance mechanisms and analyzes the influence of the power relationship between FC and their suppliers.FindingsThe results identify how external pressures from different stakeholders act on FC and FT and ST suppliers. A combination of contractual governance mechanisms (auditing, certification, assessment, code of conduct and monitoring) with relational ones (third-party, cooperation) is identified, facilitating compliance between agents. Furthermore, different power relationships (power position, level of resources and institutional distance) that influence the implementation of governance mechanisms are explored.Research limitations/implicationsThis article comprised only a systematic literature review and content analysis. Carrying out empirical research, covering the theme of this article, is the next step, which is being completed and will be discussed in due course in another publication.Practical implicationsThe results can help professionals of the FC to understand their role in multi-tier supply chain (MSC), the external pressures exerted and the governance mechanisms that can be implemented to achieve compliance.Originality/valueThis article develops three relevant issues constantly addressed in MSC, which have not yet been combined to understand the management of multi-tier suppliers.