The document discusses two cases regarding the application of EU coordination rules on social security. For Case I, the father works in Member State A while the mother and children live in Member State B. The conclusion is that family benefits should be paid in full by State A according to the priority rules. For Case II, the parents work in Member State B while the children stay in State A. The conclusion is that if the children are in State A only for studies, benefits can be paid in full by State B, but not if the children stay in other care. The document also discusses improving cooperation between the states.