In contemporary world, the digital competence of adolescents is not a separate property or capacity any longer, becoming the prerequisite and basis for many types of activities, and the Internet has become a space mediating socialization of children. Russian population study indicated that there is a «gap» in the structure of motivation to improve digital competence: although every four teenagers from five ones declare preparedness for its development, their motivation in relation to specific goals and objectives is extremely low and does not exceed 20 per cent of the maximum possible level. The paper assumes that the «gap» is caused by different contents of general and specific motivation: general motivation describes great awareness of the importance and the declared preparedness, while specific motivation refers to the setting of specific goals. Applying the Digital Competence Index (DCI) in the samples of adolescents 12-17 years old (N=1203) and of parents of adolescents of the same age (N=1208) the relationship between general and specific motivation to improve digital competences and their links to the user’s activity, confidence, emotions, self-image on the Internet and its familiarization are considered. A high level of digital competence and excessive self-confidence in the user’s skills are associated with a less general motivation. A higher level of general and specific motivation is related to the participation of teachers and parents in the development of adolescent skills in the Internet. This extremely low self-confidence and the solution of any online problems by parents are associated with passive motivation, e.g. the desire to explore the Internet spontaneously through other people. Possible methods of developing active motivation to improve digital competence and the prevention of excessive confidence in adolescents are discussed