Chemical manufacturing is conducted using either batch systems or continuous-flow systems. Flow systems have several advantages over batch systems, particularly in terms of productivity, heat and mixing efficiency, safety, and reproducibility. However, for over half a century, pharmaceutical manufacturing has used batch systems because the synthesis of complex molecules such as drugs has been difficult to achieve with continuous-flow systems. Here we describe the continuous-flow synthesis of drugs using only columns packed with heterogeneous catalysts. Commercially available starting materials were successively passed through four columns containing achiral and chiral heterogeneous catalysts to produce (R)-rolipram, an anti-inflammatory drug and one of the family of γ-aminobutyric acid (GABA) derivatives. In addition, simply by replacing a column packed with a chiral heterogeneous catalyst with another column packed with the opposing enantiomer, we obtained antipole (S)-rolipram. Similarly, we also synthesized (R)-phenibut, another drug belonging to the GABA family. These flow systems are simple and stable with no leaching of metal catalysts. Our results demonstrate that multistep (eight steps in this case) chemical transformations for drug synthesis can proceed smoothly under flow conditions using only heterogeneous catalysts, without the isolation of any intermediates and without the separation of any catalysts, co-products, by-products, and excess reagents. We anticipate that such syntheses will be useful in pharmaceutical manufacturing.