The present invention relates to a process for the production of a high melt flow propylene homopolymer or random copolymer with low odor and low volatiles content, which is suitable for thin-walled injection molding applications, said process comprising the step of polymerizing propylene and one or more optional comonomers in presence of a Ziegler-Natta catalyst comprising a titanium compound having at least one titanium-halogen bond, and a diether compound as internal electron donor, both supported on a magnesium halide in active form, an organoaluminium compound and an optional external donor.