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In Ashkenazic tradition, the first night of Selichot is held after midnight on a Motzey Shabbat night before Rosh Hashanah. This year (5782) the the slichot reading begins right after the Shabbat “Ki Tavo” (22 Elul).
The next Selichot prayers are recited in the early morning hours, before the morning prayers, in preparation for Rosh Hashanah and Yom Kippur.
In the Sephardic tradition, Selichot are said from the beginning of the month of Elul.