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Application of hesitant fuzzy sets to EQ-algebras is discussed. The notions of hesitant fuzzy prefilters (filters) and positive implicative hesitant fuzzy prefilters (filters) of EQ-algebras are introduced, and several properties are investigated. Characterizations of hesitant fuzzy prefilters (filters) and positive implicative hesitant fuzzy prefilters (filters) are considered, and conditions for a hesitant fuzzy filter to be a positive implicative hesitant fuzzy filter are investigated. Finally, the extension property for a positive implicative hesitant fuzzy filter is established.