This monograph describes methods of traditional legal means that are used in nontraditional cyberspace and how the specific implements that came into existence exactly for this purpose are applied. The aim of this research mainly concentrates at the problem with domain names, especially at Alternative Dispute Resolution. Finished Analysis of disputes resolutions over domain name .eu leads to particular conclusion of effective application of specific procedural rules in the cyberspace. Another part of this research are Trademarks and the prevention against their abuse with domain names registration and their use like key words in on line advertising of search engines.