In the first part of the work, author examines ‘Exclusion clausee’, provided for in the Article 13 of the EU Directive 2009/103/EC that relates to insurance of civil liability relating to use of motor vehicles, and duty to insure against such liability where duty of Member States was established to introduce prohibition for insurance companies to object to injured party that they do not have duty from insuranec in case of certain events occurrence relating to use or drivign of an insured motor vehicle envisaged by national regulations and insurance contract, as well as exception from that prohibition. Method how such issues were regulated in the Law on Insurance Contract of Germany and Austria was examined later.