This paper discusses how language training for refugees is implemented by the local authorities in Finland and Sweden. The responsibility, production and financing of this specific integration service, language training, is distributed over a multitude of actors in a multidimensional governance structure. We apply a conceptual framework based on intergovernmental relations and conflictual policy processes. The findings suggest that intergovernmental relations are characterized by conflicted policy processes between the actors involved in the multidimensional governance structure. Our conclusion is that insufficient financing and unclear responsibilities lead to a conflicted policy process vertically as well as horizontally.