An electrically-variable transmission is provided with input member and output member, first and second motor/generators, a first planetary gear set and a final drive gearset. Two or three torque-transmitting mechanisms that are selectively engagable alone or in different combinations to establish at least one forward electric-only operating mode including a series mode, an output split mode, and at least one neutral mode including a purely neutral mode and a neutral battery charge mode. The transmission optionally includes a one-way clutch selected from the group of friction clutch and dog clutch, or is a lockable one-way clutch, for enabling low loss forward operation, regenerative braking functionality, and/or reverse vehicle operation.