The concept of syntactic connection is fundamental for presenting the syntactic structure of any language. Linguists have described in detail the dichotomy of coordination and subordination, both from the point of view of the semantic relationships between the components of syntactic units and of the use of linguistic means to connect these components. Nevertheless, some syntactic structures have not yet received a comprehensive grammatical description. The article is devoted to the analysis of constructions with nouns being in appositive relations, as their combinations are interpreted inconsistently in modern scientific and educational literature. It has been established that the units in appositive constructions are connected on the basis of logical subordination, which appears in two variants: if the equal case ending agreement for both nouns is required in the entire paradigm, the linkage is characterized as agreement (without distributing it into complete and incomplete), if the case ending in entire paradigm is absent, it is viewed as a case (nominal) adjunction. The dependent component in parallel-case combinations of common nouns is considered to be the one that represents another name or an additional, including evaluative, attribute to the same referent that is named by the word being defined. In appositive combinations of a proper name and a common noun, the dependent component is noted to be the one expressed by a proper name of any type. The syntactic function of the dependent components in appositive phrases is suggested to be characterized without employing the concept of apposition, thus treating them as coordinated or uncoordinated attributes.