The compilation of the Avesta in the Avestan alphabet has been assigned to different periods of the Sasnnian rule, or even to the early Islamic period; Here, the author rediscusses the evidence provided by Pahlavi books and other sources, which in great majority point toward the existence of a Sasanian Avesta. In the second part of the article, he aims at demonstrating that the cursive variant of the Pahlavi alphabet was already in use by the very end of the 5th cenlllry AD or, at the latest, by the beginning of the 6th century