This article examines the potential and features of the formation at the university of future teachers of professional readiness to develop and transmit family values to students. The relevance of the topic is determined by the crisis state of the modern family and the need to broadcast the values of the traditional family to the younger generation. The author understands the peculiarities of this process as the originality of the modern generation of youth, the specifics of the activities of teachers of pedagogical training profiles at the university, as well as a set of targeted, substantive and procedural features that are modified in the situation of transformation of the axiosphere of a modern citizen. The set of personality-oriented, socially-oriented, civic-oriented, artistically-oriented, reflexively-oriented and professionally-oriented groups of family values highlighted by the author is purposefully formed in the selected educational conditions of family communication, leisure activities, public associations, as well as organizations of general, additional and vocational education. Examples of family education on educational platforms with virtual content, examples of the use of hackathons in university education, a professional skills competition, and STEAM design are considered. Generalized features of the formation and transmission of family values to students by future teachers in university education (adaptability to a specific place, time, amount of study load, hybridity, continuity, the ability to return to some material, personalized pace, volume, style and support of education with the possibilities of self-government and its adjustments) arouse interest among modern students and increase their professional motivation.