The European national health systems - Bismarckian pay-as-you-go systems as well as Beveridge systems financed by taxes - are characterized by redistribution within and between generations. Both types are more or less similar in their mode of functioning and both bear inefficiencies in many fields. The lack of resistance towards demographical changes is a threat for the stability of these systems, even without migration. Yet in a world with migration, the problem of instability has to be considered also from a different angle. Competition of health systems could induce financial difficulties or even the collapse of redistribution within these systems. This problem is even more relevant if the Enlargement of the Union continues and heterogeneity of the social and medical services granted by the states grows. Which measures have therefore to be taken to stabilize the national health systems within the European Union, where the right of freedom of movement is granted to every citizen? Is harmonization or even centralization an efficient solution to choose? In this article it is argued that reforms of the national health systems are necessary to overcome the problems induced by migration. The main step to be taken is the separation of both the intragenerational and the intergenerational distribution from the insurance system. This is inevitable to provide an efficient health care system at the national level and to insure the freedom of movement in the European Union without undermining the solidarity of the insurance pool.