Kinship term systems (KTS) are one of the most attractive and well-studied topics in anthropology and linguistics. Although in most Indo-European languages kinship terminology in the synchronic perspective is described quite well, the dynamics of the transition of one system into another, not to mention the reconstruction of Proto-Indo-European KTS, is still a field of hypotheses. The authors of the article make an attempt to trace the evolution of KTS s in the three branches of the Indo-European language family with a long written tradition — Greek, Latin- Romance and Indian — on the basis of actually recorded terms, rather than hypothetical reconstructions, which are usually insufficient for a clear typologization of the systems. Only kinship terms denoting intragenerational relationships between parents (including their siblings) and children (including their siblings and cousins), which are key to identifying KTS types within a generally accepted typology, were analyzed. For each language branch, observations were made on kinship terms in three time periods — ancient, medieval and modern. To reveal the semantics of terms in diachronic perspective, in some cases their etymological analysis and the corpus study were performed, and the evidence of ancient and modern lexicographers was used. The obtained data were integrated into a typological matrix, allowing us to make an assumption about the kinship term systems dominating at a particular time period. The results of the study allow us to speak about the possible direction of KTS development in the analyzed branches of languages, viz. evolution from the initial Sudanese system in the most ancient languages, through the transitional medieval stage to the later Eskimo system is observed. The paper shows that, given a common vector of development, these processes proceeded at different speeds and not always linearly in different branches. In addition, the question of the possibility of identifying rudiments of the Iroquoian system in the analyzed languages is discussed, and the debatable problem of the relevance of the Omaha type for the Proto-Indo-European language is touched upon.