Longman Dictionary of Contemporary English
modal auxiliary
noun
EXAMPLES FROM CORPUS
▪ The use of dare as a modal auxiliary follows the same pattern as need.
The Collaborative International Dictionary
modal auxiliary
modal auxiliary \mo"dal aux*il"iar*y\(Gram.), n. Any one of the auxiliary verbs of English, such as can, may, will, shall, must, might, could, would, or should, which are used together with the infinitive form of another verb to express distinctions of mood[2], such as uncertainty, possibility, command, emphasis, and obligation.
Wiktionary
modal auxiliary
n. (context grammar English) A verb used to express the mood (or tense) of another verb.