Tanna Devei Eliyahu (Hebrew: תנא דבי אליהו; alternate transliterations include Tana D'vei Eliyahu and Tana D'vei Eliahu) is the composite name of a midrash, consisting of two parts, whose final redaction took place at the end of the 10th century CE. The first part is called "Seder Eliyahu Rabbah" (31 chapters); the second, "Seder Eliyahu Zuṭa" (15 chapters). A distinct reference to this midrash occurs in the Talmud in Ket. :
Elijah used to come to R. Anan, upon which occasions the prophet recited the Seder Eliyahu to him. When, however, R. Anan had given this decision [one previously narrated in the Talmud] the prophet came no more. R. Anan fasted in consequence, and begged forgiveness, whereupon the prophet came again; but R. Anan had such great fear of Elijah that, in order to avoid seeing him, he made a box and sat in it until the recitation was over (but see R. Anan).
Hence, according to Rashi, the midrash has the two names, "Rabbah" for the earlier, and "Zuṭa" for the later lectures. Anan was a Babylonian amora of the 3rd century. The collection of baraitot concerning him, referred to in this midrash, is cited in the Babylonian Talmud under the title "Tanna debe Eliyahu" (see below), and the utterances in question are found in the midrash itself. The tosafot to Ketubot (106a, s.v. והיינו) say that the midrash consists of a large book and a small one. R. Nathan ben Jehiel in his Aruk (s.v. סדר, ii.) says: "The midrash contains baraitot which the prophet taught to Anan, and consists of two parts, a large seder with 30 chapters, and a small seder with 12 chapters; and all of the Tanna debe Eliyahu cited in the Talmud is to be found in these baraitot." The inner connection between these two midrashim is a loose one, and it is only in sections 5 to 10 that the second refers to the first.