The invention relates to a process for converting feeds composed of hydrocarbons by thermal steamcracking to at least one olefin-containing product stream comprising at least ethylene and propylene, with at least partial conversion of the feeds in at least one first cracking furnace (1) and in at least one second cracking furnace (2). According to the invention, a fresh feed (B) is fractionated into at least one first and one second fresh feed fraction (B1, B2), and the first fresh feed fraction (B1) is conducted at least partly into the first cracking furnace (1) and the second fresh feed fraction (B2) at least partly into the second cracking furnace (2).
