We introduce a new matching model to mimic two-sided exchange programs such as tuition and worker exchanges, in which export-import balances are required for longevity of programs. These exchanges use decentralized markets, making it difficult to achieve this goal. We introduce the two-sided top-trading-cycles, the unique mechanism that is balanced-efficient, worker-strategy-proof, acceptable, individually rational, and respecting priority bylaws regarding worker eligibility. Moreover, it encourages exchange, because full participation is the dominant strategy for firms. We extend it to dynamic settings permitting tolerable yearly imbalances and demonstrate that its regular and tolerable versions perform considerably better than models of current practice.