There are some closely related grammatical categories that are in a very strict semantic and syntagmatic connection. Their grams are determined by each other, and that leads to emergence of a complex grammatical system whose elements are tied up not only paradigmatically, but also hierarchically. The paper presents a new theoretical approach to such type of systems based on the data from some of the modern Mayan languages. In order to describe grammatical systems of this type a concept of «interpreting» grammatical category is introduced. For comparative reasons, the similar language phenomena from Indo-European, Nakh-Daghestanian, and Tibeto-Burman languages are analyzed.