In the article, the idea is put forward that in the phraseological system of the Azerbaijani language, alliteration and assonances are less active in the manifestations than in other languages. Comparative analysis of theonyms and demonims in composite phraseological units in the Azerbaijani language shows that a sufficient degree of functionality is demonstrated here not only by the presence of types of sound reproduction of both sound repetitions, but also by the widespread joint (alliterativeassonance) model of figurative phonetic image techniques.