The invention relates to a process for converting hydrocarbon feeds by thermal steamcracking to at least one olefin-containing product stream comprising at least ethylene and propylene, with at least partial conversion of a first hydrocarbon feed in at least one first cracking furnace (1) and of a second hydrocarbon feed in at least one second cracking furnace (2). According to the invention, the second hydrocarbon feed comprises predominantly hydrocarbons having a carbon number of 5 or/and 4 and consists for the most part of one or more recycled fractions (P, T) which are obtained from the product stream, and the second hydrocarbon is converted in the second cracking furnace (2) with cracking conditions that lead to a ratio of propylene to ethylene of 0.7 to 1.6 kg/kg.