In recent years, scholars have increasingly turned their attention to the separate areas of corporate social responsibility (CSR) and supply chain management (SCM). However, little scholarly attention has been paid to the transmission of CSR requirements from a small to medium-sized enterprises (SME) perspective. Drawing on institutional and innovation diffusion theories, this paper investigates to what extent the CSR requirements of customers influence the CSR activities of SMEs and their CSR requirements toward their own suppliers. Multiple mediation analysis was performed on data from a sample of 146,060 French SMEs. The findings indicate that the CSR requirements of customers have a direct negative effect on SMEs’ CSR requirements toward suppliers. However, the relationship becomes positive when we take into account the mediating role of the SMEs’ own CSR activities (i.e. economic, social and environmental activities). Furthermore, the study reveals that the indirect effect through economic CSR activities is the greatest, followed by social and then environmental CSR activities. Our main contribution is that implementing CSR activities within SMEs is a necessary step so that SMEs can be brokers in the transmission of CSR requirements in the supply chain.