The paper deals with the application of the current Russian criminal procedure legislation to criminal processes involving persons with limited cognitive abilities as a form of realizing the social responsibility of the modern state of law to its citizens. The paper studies the mechanism for ensuring the rights and legitimate interests of participants in criminal proceedings with limited cognitive capabilities. It also formulates practical proposals to improve this mechanism taking into account the provisions of the international law and the concept of modern legal understanding of the essence of the social state. The authors base their position on a compensatory approach, which allows ensuring the most equal opportunities for the participation of persons with limited cognitive abilities in criminal proceedings, without diminishing the rights of other participants. This approach may be applied not only to the category of persons in question: it is generally aimed at ensuring the enforcement of the rights of participants in criminal proceedings who have limited abilities. However, due to the limited scope, this paper only considers one category of such participants, which is the largest in terms of quantitative indicators, since it includes minors, persons of older age groups, persons with mental disorders, mental illnesses, persons being in physiological conditions that affect the level of their cognitive functions, etc.