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General Motors has introduced a Two-Mode Transmission (2-MT) that provides significant improvements over the Toyota THS-II transmission. These improvements are achieved by employing additional planetaries with clutches and brakes to switch from a Mode-1 to Mode-2 as vehicle speed increases. In addition the 2-MT has four fixed-gear ratios that provide for a purely mechanical energy path from the IC engine to the driven wheels with the electric machines also able to provide additional driving torque. The purpose of this present paper is to extend the methodology in a previous paper [1] to include the 2-MT, thereby presenting an analytic foundation for its operation. The main contribution in this analysis is in the definition of dimensionless separation factors, defined in each mode that govern the power split between the parallel mechanical and electrical energy paths from the IC engine to the driven wheels.