The author discusses the semantic and syntactic features of lexemes 'mozhet (Russ.), byt' mozhet (Russ.)', 'mozhe (Pol.), byc' mozhe (Pol.)'. They express speaker's own attitude to the message: they signify possibility, probability of a fact, incident. What is more, they may contain a shade of a question or suggestion. The above-mentioned modal lexemes are used in the meaning: 'if something may/might happen or may/might be true, there is a possibility that it will happen or be true but it is not certain'. Their modal meaning can be transformed into a statement: 'I think, we can suppose that...'. Sentences with such modal lexemes are usually of two-element structure: dictum (D) i.e. the part of a sentence that names facts (processes or incidents), and modus (M) that names the speaker's own attitude to the indicated facts, so it explains how we should treat dictum. Apart from the Polish direct dictionary equivalents of the Russian lexeme other synonymous forms with the same shade of modal meaning: 'bodaj; mozhliwe, zhe...' appear only in several examples. The lexemes either refer to the sentence as a whole or to some of its elements.