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We present a class of Multicommodity Flow Problems with Commodity Compatibility Relations (MCFP-CCR), in which compatibility relations among commodities used at each node are required. This class of problems has application in the Train Unit Scheduling Problem (TUSP) [1, 2], where train units of different traction types may not be coupled with each other to serve the same train trip. Computational complexity issues are discussed and solution methods are proposed. Computational experiments using the proposed solution methods are reported.