A process for producing C2 and C3 hydrocarbons by a) subjecting a mixed hydrocarbon stream comprising a middle distillate to first hydrocracking to produce a first hydrocracking product stream, b) subjecting a second hydrocracking feed stream to second hydrocracking to produce a second hydrocracking product stream, wherein the second hydrocracking is more severe than the first hydrocracking and c) subjecting a C4 hydrocracking feed 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, wherein the C4 hydrocracking is more severe than the second hydrocracking. The first hydrocracking product stream, the second hydrocracking product stream and the C4 hydrocracking product stream are fed to a separation system.