Although many people seem to share the intuition that multinational companies (MNEs) carry a responsibility for the working conditions in their supply chains, the justification offered for this assumption is usually rather unclear. This article explores a promising strategy for grounding the relevant intuition and for rendering its content more precise. It applies the criteria of David Miller's connection theory of remedial responsibility to different forms of supply chain governance as characterized by the Global Value Chains (GVC) framework. The analysis suggests that the criteria for identifying MNEs as remedially responsible for bad working conditions in their direct suppliers are fulfilled in many cases, even though differentiations are required with regard to the different supply chain governance structures. MNEs thus have a duty to make sure currently bad working conditions in their suppliers are changed for the better. Moreover, since production in supply chains for structural reasons continuously generates remedial responsibility of MNEs for bad working conditions in their suppliers, it puts the prospective responsibility on them to make sure that their suppliers offer acceptable working conditions. Further, it is suggested that the remedial responsibility of MNEs might require them to make financial compensation to victims of bad working conditions and in grave cases initiate or support programs to mitigate disastrous effects suffered by them.