A propulsion system for a pedal vehicle and comprising: - a first deformable transmission element arranged to drive a rear wheel of the pedal vehicle; - a powertrain comprising: • a crankset axle arranged to rotate about a first axis of rotation, • a main output plate arranged to drive the first deformable transmission element, • a first motor, • a second motor, • an epicyclic gear train comprising a first input element, an output element and a sun, the crankset axle and the second motor being connected to the epicyclic gear train via the first input element so as to form a first input of the epicyclic gear train, the first motor being connected to the epicyclic gear train via the sun so as to form a second input of the epicyclic gear train, the output element connecting the epicyclic gear train to the main output plate so as to form an output of the epicyclic gear train, and the first deformable transmission element being arranged to transmit power between the powertrain and the rear wheel of the pedal vehicle; and - a casing assembly; - a rear sprocket; - the main output plate, the first input element, the output element and the sun being arranged so as to rotate about a same second axis of rotation different from the first axis of rotation; characterised in that: - the powertrain comprises: • a secondary output plate arranged to rotate about the first axis of rotation and meshed to the first deformable transmission element, • a speed reduction system maintaining the direction of rotation for transmitting a rotation between the crankset axle and the first input element; and - the first deformable transmission element, a portion of the crankset axle, the main output plate, the first motor, the second motor, the epicyclic gear train, the secondary output plate, and the rear sprocket are within the casing assembly. - a first deformable transmission element arranged to drive a rear wheel of the pedal vehicle; - a powertrain comprising: • a crankset axle arranged to rotate about a first axis of rotation, • a main output plate arranged to drive the first deformable transmission element, • a first motor, • a second motor, • an epicyclic gear train comprising a first input element, an output element and a sun, the crankset axle and the second motor being connected to the epicyclic gear train via the first input element so as to form a first input of the epicyclic gear train, the first motor being connected to the epicyclic gear train via the sun so as to form a second input of the epicyclic gear train, the output element connecting the epicyclic gear train to the main output plate so as to form an output of the epicyclic gear train, and the first deformable transmission element being arranged to transmit power between the powertrain and the rear wheel of the pedal vehicle; and • a crankset axle arranged to rotate about a first axis of rotation, • a main output plate arranged to drive the first deformable transmission element, • a first motor, • a second motor, • an epicyclic gear train comprising a first input element, an output element and a sun, the crankset axle and the second motor being connected to the epicyclic gear train via the first input element so as to form a first input of the epicyclic gear train, the first motor being connected to the epicyclic gear train via the sun so as to form a second input of the epicyclic gear train, the output element connecting the epicyclic gear train to the main output plate so as to form an output of the epicyclic gear train, and the first deformable transmission element being arranged to transmit power between the powertrain and the rear wheel of the pedal vehicle; and - a casing assembly; - a rear sprocket; - the main output plate, the first input element, the output element and the sun being arranged so as to rotate about a same second axis of rotation different from the first axis of rotation; characterised in that: - the powertrain comprises: • a secondary output plate arranged to rotate about the first axis of rotation and meshed to the first deformable transmission element, • a speed reduction system maintaining the direction of rotation for transmitting a rotation between the crankset axle and the first input element; and • a secondary output plate arranged to rotate about the first axis of rotation and meshed to the first deformable transmission element, • a speed reduction system maintaining the direction of rotation for transmitting a rotation between the crankset axle and the first input element; and - the first deformable transmission element, a portion of the crankset axle, the main output plate, the first motor, the second motor, the epicyclic gear train, the secondary output plate, and the rear sprocket are within the casing assembly.