An electrically-variable transmission has four motive elements, including an input member, an output member, and first and second motor/generators. The transmission also has two differential gear sets, and four selectively engagable torque-transmitting mechanisms. All members of each differential gear set have at least one of the motive elements connectable therewith. The input member and one motor/generator are both connected or connectable with the same member of one of the differential gear sets, and the output member and either of the motor/generators are both connected or connectable with the same member of the other one of the differential gear sets. The torque-transmitting mechanisms are selectively engagable in combinations of two to establish input-split and output-split electrically-variable modes of operation.