The growing market of the cyber space remains insecure, and right to property in it - in danger. This work has focus on the cyber crimes as threat to property. It analyses national (US, Ukraine) and international framework of the approaches to property and its legal protection from cyber crimes and draws recommendations how property in cyber space can be secured better. The Chapter I talks on the nature of the cyber crimes, their types and the relationship with property. It then explains how differently the property is viewed in common and civil law countries. The Chapter II continues with anti-cyber crime efforts of international organizations with special attention to the Council of Europe Convention on Cybercrime and then concludes with two national systems: American and Ukrainian one. The helpful bibliography is added.