We examine the relationship between relative demands for skills, non-routine, and non-offshorable tasks in Swedish MNE parents (onshore) and their employment shares in affiliates abroad (offshore). Our estimations suggest that increased employment shares in affiliates abroad (offshore) result in higher relative demand for skills and larger shares of non-routine tasks performed by employed that are highly educated in the parents at home (onshore). However, we do not find any evidence for that the share of non-offshorable tasks rises in the parents of Swedish MNEs when employment shares increase in their affiliates overseas. Furthermore, we estimate the relationships between absolute employment onshore (skilled and less-skilled labour) and employment in affiliates offshore (high- and low-income countries). Increased employment in affiliates in low-income countries relates negatively to the employment of less-skilled workers in manufacturing MNE parents (substitute), whereas increased employment in affiliates in high-income countries correlates positively with the employment of skilled workers in service MNE parents (complement).