The article examines the verbs included in the structure of the semantic field of thinking, namely the basic verbs to think and thinking, complicated by the prefix y-, based on the material of Russian texts of different genres. The subject of the study is the following values of situational modality (the so–called semantic X) - the invariant value of desirability, as well as the value of the opportunity realized by derivatives to conceive, to think in the process of communication. The purpose of the work is to reveal the specifics and conditions of the modal functioning of these verbs. Achieving this goal is facilitated by solving the following tasks: 1) to identify the modal meanings realized by the considered derivatives; 2) to determine the conditions of their modal functioning within the framework of the utterance; 3) to identify the role of the nominatively independent word-formation with formant y- in the process of creating the modal, modal-evaluative meanings of the corresponding derivatives. The goals and objectives of this work determined the choice of a comprehensive research methodology, including the following methods: functional-semantic, descriptive, contextual. The scientific novelty of the article is determined by the subject of the study. As a result of the conducted research, it is concluded that the verbs of thinking, to think with the formant y- are able to realize the modal meanings of possibility, desirability (which is a condition for the realization of opportunity), associated mainly with intentions that contradict the moral, ethical, social norms of society. The analysis of the texts made it possible to determine the lexical and grammatical basis of the modal functioning of the verbs of thinking, complicated by the prefix y-, in the semantics of which the modal component is implicitly contained, to establish syntactic conditions for the realization of the meanings of situational modality, i.e. the presence of a dependent subject semantically unlimited infinitive in the verb. The reinforcing role of the service formant is determined for the formation of the modal meaning of the derivatives to think, to conceive as an independent (autonomous) significant unit, in the meaning of which the seme "bringing to an undesirable state" is explicitly expressed, as well as the pejorative seme "to commit something bad, criminal, reprehensible (to the detriment of someone)". The materials of the article can be used at seminars and practical classes of the university on topical issues of the category of linguistic modality.