The purpose of this work is to introduce the notion of synthesizing mass-exchange networks (MEN's). A systematic, two-stage, procedure is proposed for the synthesis of cost-effective MEN's. In the first stage, a thermodynamically-oriented procedure is used to identify the thermodynamic bottlenecks (pinch points) that limit the extent of mass exchange between the rich and the lean process streams. Preliminary networks, that feature maximum mass exchange, are generated at this stage. The objective of the second stage is to improve the design of these preliminary networks so as to develop a final configuration of the MEN that satisfies the assigned exchange duty at minimum venture cost. This approach is applied to the synthesis of MEN's with single-component targets as well as multicomponent, compatible targets. An illustrative example on the sweetening of coke-oven gas is presented to demonstrate the applicability of the proposed synthesis procedure.