General Motors has recently developed a front-wheel drive version of its two planetary two-mode transmission (2-MT) for a hybrid-electric vehicle powertrain . This newer transmission includes two planetary gears with two transfer clutches and two braking clutches. With activation of designated pairs of these four clutches, four fixed-gear ratios between the transmission's input shaft and output shaft are obtained. In addition, activation of specific individual clutches gives two modes of operation whereby the IC engine speed is decoupled from the vehicle velocity thus providing an electrical continuously variable transmission (ECVT). This present paper extends the power-split analysis in  by deriving a safe-operating region (SOR) in the plane of IC engine speed vs. vehicle velocity for the four fixed-gear and two ECVT modes. This SOR is bounded by the speed limitations of the 2-MT components. Similar results are presented for the Toyota Hybrid System II (THS-II) transmission. Also developed is the vehicle velocity limit for both the 2-MT and the THS-II transmissions under battery electric vehicle (BEV) operation.