The invention relates to a process for producing C2 and C3 hydrocarbons, comprising a) subjecting a mixed hydrocarbon feedstream to first hydrocracking in the presence of a first hydrocracking catalyst to produce a first hydrocracking product stream; b) separating the first hydrocracking product stream to provide a light hydrocarbon stream comprising C4− hydrocarbons and c) subjecting the light hydrocarbon stream to C4 hydrocracking in the presence of a C4 hydrocracking catalyst to obtain a C4 hydrocracking product stream comprising C2 and C3 hydrocarbons.