A hybrid powertrain is provided that includes an engine operatively connected with an input member. The powertrain includes a transmission with first and second electric motor/generators, a differential gear set having multiple members, and selectively engageable torque-transmitting mechanisms. The input member, the output member, the engine and the motor/generators are selectively interconnected through the differential gear set by engagement of the torque-transmitting mechanisms in different combinations. An electronic controller controls the electric motor/generators, the engine and the torque-transmitting mechanisms to provide multiple operating modes between the input member and the output member, including an electric-only operating mode in which the engine is off and one motor generator acts as a motor to provide torque at the output member while the other electric motor/generator can remain substantially stationary, and another electric-only operating mode in which both electric motor/generators act as motors to provide torque at the output member.