The invention relates to a method for carrying out heterogeneous catalytic exothermic gas phase reactions at a high temperature and high pressure, during which the synthesis gas comprised of a mixture of make-up gas and/or of recycle gas is fed through at least two synthesis stages that are connected in-series to form a synthesis system. The product gases from the synthesis stages, with the exception of the last stage, are separated into at least two partial flows. One partial flow is cooled until the product is condensated out, and the condensate containing the product is separated from the gaseous constituents. Afterwards, the gaseous constituents are combined with the warm portion of the product gas in order to reach the inlet temperature of the next synthesis stage. In addition, the partial flow from which the product was condensated out and removed, can be heated before being remixed with the warm portion of the product gas. After heating, the temperature is less than that of the warm portion of the product gas, and the heat used for heating the partial flow from which the product was condensated out, is extracted, at least in part, from this partial flow during its cooling.