The first Selichos tefillah for Sephardim was on Monday night although the large crowd that gathered at the Kosel was comprised of Jews from all stripes.
Sephardim begin reciting Selichos at the beginning of Elul in order to recite them for a period of 40 days, the same period of time that Moshe Rabbeinu was on Har Sinai.
Ashkenazim begin reciting Selichos on the Motzei Shabbos (or Sunday morning) before Rosh Hashanah, but if there are less than four days between the beginning of Selichos and Rosh Hashana, then Selichos begins on the previous Motzei Shabbos.
(YWN Israel Desk – Jerusalem)