An apparatus for separation or synthesis of process substances is configured with at least two cell stacks, within each of which there is arranged at least one large-area layer for the separation or synthesis and passages are formed for feeding and discharging at least one process substance to or from the at least one layer. To ensure that the ratio of active surface area to total area of the layer is as high as possible yet on the other hand that uniform distribution of at least one process substance over the layer are ensured, at least two passages for a process substance are formed within at least a first cell stack, of which a first passage is used to pass the process substance through the first cell stack to a second cell stack and of which the second passage is used to feed or discharge the process substance to or from the at least one layer in the first cell stack.