A process for the manufacture of a modified titanium-containing component of a Ziegler-Natta catalyst for the polymerization of C3-6 .alpha.-monoolefins, wherein a specific titanium-containing compound and a specific phosphorus-containing compound are dry-milled at a specific grinding acceleration in a vibratory ball mill, The characteristic feature of the process of the invention is that a mill is used which has a specific useful volume and the mill is initially charged with a specific amount of the titanium-containing compound, which is milled at a low temperature while the phosphoruscontaining compound is gradually added, whereupon milling is continued while the temperature of the process material is gradually raised to a specific value and maintained at said value for a specific period of time, whereupon, if desired, milling is again continued at a lower temperature for a specific period of time. In this manner, modified titaniumcontaining components are obtained which in the polymerization process produce highly reproducible yields of polymer.