In order to maintain the variations in the quantity of additive supplied, caused by pressure fluctuations in the system, within negligible limits during the production of a polyurethane reaction mixture made of fluid reaction components and an additive, in particular an expanding agent, the supply line (4) that leads to the mixing head (6) is subdivided into a main line (8) and a secondary line (9) and the additive is supplied into the secondary flow, which is essentially smaller than the main flow.