The article deals with the issue of the parental control over the behaviour of their children in the cyberspace and analyses the conflict of the parents' right (and obligation) to ensure the proper emotional, intellectual, and moral development of the child on the one hand, and child's right to access and seek information and child's privacy on the other hand. The article aims to define the scope and limits of parental responsibility with respect to the rights of the child and further seeks to assess the appropriateness of using special tools of parental control relating to a child's use of the Internet.