The relevance of the study is caused by the paramount importance of the legal responsibility institution, without which one cannot imagine the existence of the legal state. Threading all the spheres of public life, the legal category of responsibility is a significant element of the mechanism for their regulation and plays an important role in the provision of order and safety. The objective of the paper is in the cognition of the complicated and multi-faceted phenomenon of legal responsibility and in the definition of its position in the legislative system of the Republic of Kazakhstan. In this regard, this paper is aimed at the revealing of the main approaches towards the understanding of the responsibility in law, the study of the kinds of legal responsibility and their legal sources. The leading approach in the study is the analysis that allows integrally considering the accumulated theoretical experience in the issues of legal responsibility, as well as revealing the drawbacks in the documentation of the responsibility in the applicable legislation. The paper presents modern concepts of legal responsibility, reveals the existing definitions of its concept, and considers the system of legal responsibility and its basic elements (kinds) with the definition of its legal framework for each element of the responsibility. The materials of the paper may be helpful to the scientists in their research of the problems of legal responsibility in all the legal branches, university teachers and students in the educational process when studying and teaching the legal disciplines.