A harmonic drive system for a pedal-electric-cycle comprises a transmission gear device including a wave generator assembled by an elliptical cam and a flexible bearing, a flexible-flexspline, a rigid-circular-spline having rigid-circular-spline internal gear teeth, a gear set, and a one-way clutch having an inner surface defining a space for containing a spindle of the pedal-electric-cycle. A first end of the flexible-flexspline has flexible-flexspline external gear teeth for meshing with the rigid-circular-spline internal gear teeth and an inner surface defining a space for containing the wave generator. The gear set has a first input portion connected to a second end of the flexible-flexspline, a second input portion having an inner surface defining a space for containing the one-way clutch, and an output portion connected to a sprocket of the pedal-electric-cycle. The first input portion has a first-input rotational axis. The second input portion has a second-input rotational axis.