Abstract: A process for producing a modified polypropylene by copolymerizing propylene with ethylene in the presence of a Ziegler-Natta catalyst is provided.This process consists of the following three steps:a first step of carrying out polymerization so as to give a propylene polymer corresponding to 75-90% by weight based on a final modified polypropylene and having an ethylene content of 2% by weight or lower,a second step of preparing an ethylene-propylene random copolymer (A) having an intrinsic viscosity of 12 dl/g or higher and an ethylene content of 50-95% by weight; anda third step of preparing an ethylene-propylene random copolymer (B) having an intrinsic viscosity of 9.5 dl/g or lower and an ethylene content of 40-90% by weight,the proportion of said (A) in the total amount of said (A) and (B) being adjusted to 4-30% by weight. In this process, it is possible to prepare said (B) in the second step and then prepare said (A) in the third step.