Reactor for conducting exothermic equilibrium reactions, in which a gaseous feed mixture is at least partly converted over a solid catalyst to a product mixture comprising at least one liquid reaction product condensable at the reactor pressure and at temperatures below the reactor temperature, comprising at least two series-connected reaction cells that are in fluid connection with one another and are arranged in a common reactor shell, wherein each reaction cell comprises the following series-connected assemblies that are in fluid connection with one another: (a) a preheating zone suitable for heating the feed mixture or the gaseous product stream from the upstream reaction cell, wherein the preheating zone can optionally be dispensed with in the first reaction cell in flow direction of the gaseous feed mixture, (b) at least one reaction zone comprising a catalyst active in respect of the exothermic equilibrium reaction to be conducted as catalyst fill in a catalyst bed and a cooling apparatus in a heat-exchanging relationship with the catalyst bed, (c) at least one cooling zone comprising a cooling apparatus suitable for cooling the partly converted, gaseous product stream that has been laden with condensable reaction product and exits from the reaction zone to a temperature below the dew point of this gas, (d) a deposition zone comprising a phase separation apparatus for separation of the product stream that exits from the cooling zone into a gaseous product stream that has been freed of condensate and a condensate stream comprising liquid reaction product, (e) means of discharging the condensate stream comprising liquid reaction product and optionally means of feeding the condensate stream to a workup apparatus for the reaction product, (f) means of discharging the gaseous product stream that has been freed of condensate and means of feeding this gaseous product stream to a subsequent reaction cell arranged downstream and/or means of discharging the gaseous product stream from the reactor. (a) a preheating zone suitable for heating the feed mixture or the gaseous product stream from the upstream reaction cell, wherein the preheating zone can optionally be dispensed with in the first reaction cell in flow direction of the gaseous feed mixture, (b) at least one reaction zone comprising a catalyst active in respect of the exothermic equilibrium reaction to be conducted as catalyst fill in a catalyst bed and a cooling apparatus in a heat-exchanging relationship with the catalyst bed, (c) at least one cooling zone comprising a cooling apparatus suitable for cooling the partly converted, gaseous product stream that has been laden with condensable reaction product and exits from the reaction zone to a temperature below the dew point of this gas, (d) a deposition zone comprising a phase separation apparatus for separation of the product stream that exits from the cooling zone into a gaseous product stream that has been freed of condensate and a condensate stream comprising liquid reaction product, (e) means of discharging the condensate stream comprising liquid reaction product and optionally means of feeding the condensate stream to a workup apparatus for the reaction product, (f) means of discharging the gaseous product stream that has been freed of condensate and means of feeding this gaseous product stream to a subsequent reaction cell arranged downstream and/or means of discharging the gaseous product stream from the reactor.