The article discusses the problem of the pupils' and students' dependence on the Internet use (the Internet addiction). The historical aspect of the emergence and identification of Internet addiction as a mental disorder is considered. The main types of Internet-based dependencies are described; there are the next types of them: computer-based dependency, compulsive navigation in the network, information overload, cyber-sexual and cyber-communicative addictions. It was revealed that cybercommunicative addiction is the most common type of Internet dependence among young people. It was suggested that there is a connection between the spending time in network and the attention concentration level of the young generation. The study revealed the features of concentration and attention at the presence of the Internet and cyber-communicative addictions. The resulting statistical sample was processed using various techniques aimed at identifying the attention stability level, work efficiency and degree of working persons' in. The performed analysis of the results confirms the hypothesis.