A process for conducting exothermic equilibrium reactions, especially for the performance of methanol synthesis by heterogeneously catalysed conversion of synthesis gas, is proposed, which enables readjustment and hence optimization of the reaction conditions along the longitudinal coordinate of the reactor. For this purpose, in the process according to the invention, a reactor is used which is divided into a multitude of series-connected reaction cells, each of which comprises a preheating zone, a cooled reaction zone, one or more cooling zones and a deposition zone for condensable reaction products. In this way, the reaction conditions are adjustable to the respective, local composition of the reaction mixture and variable over the reactor length.