Parenthood can be a source of stress, especially for parents with young children. For migrants, the task is made more complex by cultural differences and the child's integration into a psychic filiation. Traditionally, parents rely on a social group to help them cope with the demands of parenthood. However, this support may be lacking in migratory situations. The literature in psychology has little data available on the composition of social support networks, particularly for transnational networks. The aim of this study is therefore to explore both the local and transnational support networks for migrant parents with respect to a sense of stress for parents. The sample consisted of 62 migrant parents living in Switzerland, and a quantitative and qualitative methodology was used to analyze the data. The results revealed that migrant parents maintain both local and transnational social networks to cope with the challenges of parenting. First-time arrivals have a less well-developed local support network and a corresponding higher level of parental stress. The density of the local support network increases with the duration of residency in Switzerland.