A series electric drivetrain includes a multiple speed, mechanically-shifted transmission driven by a pair of electric motors (12,14). Input power is provided by both electric motors during operation in any given speed ratio, and by only one of the electric motors during shifting between speed ratios. During shifting, the motor not providing input power is released from the output, and accelerated or decelerated to a post-shift speed. When the released motor reaches the post-shift speed, a clutch (C1-C4) is synchronously engaged to complete the shift, and the motors resume a shared supply of the transmission input power.