The article considers non-agreeing attributes in an oblique case modifying a noun that names a person (i. e. a person noun), an object, or space as well as their semantics, textual functions, and the problem of detachment. The aim is to show the dependence of the detachment problem on the text functions fulfilled by a non-agreeing attribute. As a rule, it is non-detached attributes which serve as a means of expressing the semantic category of definiteness. The category of definiteness/indefiniteness manifests itself as a textual category in this part of the language system. A non-agreeing attribute referring to a person is more often used when introducing new characters or a new view of them. Such text fragments are reproductive; they are usually organised by the observer’s point of view. A non-agreeing attribute can join a sequence of other attributes which it is connected with through different relationships such as clarifying, cause-effect, extending, and others. The problem of the number of attributes modifying a noun referring to a person is associated with the viewpoint issue, i. e. different extent of the observer’s interest in the depicted character. The important/unimportant (random) depicted character criterion turns out to be significant for describing non-agreeing attributes. Object and spatial nouns also function as indefinite in the context of non-agreeing attributes. Attributes modifying them name significant features of the object and convey the idea of definiteness.