The invention relates to a process for producing C2 and C3 hydrocarbons, comprising a) subjecting a mixed hydrocarbon stream to first hydrocracking in the presence of a first hydrocracking catalyst to produce a first hydrocracking product stream; and b) subjecting the first hydrocarbon product stream to C4 hydrocracking optimized for converting C4 hydrocarbons into C3 hydrocarbons in the presence of a C4 hydrocracking catalyst to obtain a C4 hydrocracking product stream comprising C2 and C3 hydrocarbons.