Abstract: Olefins or mixtures of olefins, particularly propene or mixtures of propene advantageously with ethene, can be polymerized using a Ziegler-Natta catalyst system containing, besides a transition-metal-based procatalyst and cocatalyst which is an organometallic compound, a compound particularly suited for controlling the stereospecificity of the produced polymer. Such a compound called an external donor may also have other effects. By using an acetal derivative of an aldehyde that has two ether groups for this purpose, advantageously selected from the group of dialkoxyphenylalkanes, e.g., dimethoxyphenylpropane, a good stereospecificity of the product is attained combined with the high hydrogen sensitivity of the catalyst system, whereby the use of hydrogen as the chain transfer agent offers an easy control method of the molecular weight of the product by means of adjusting the amount of hydrogen available in the polymerization reaction.