Electric bicycle comprising: - a rear wheel provided with a wheel axle mounted in a hub; - a rear portion of the frame having two seat stays (20, 21) that are spaced apart from one another so as to define the space for receiving the rear wheel; - a crankset that is designed to be actuated by the muscular force of a user in order to transform that force into a pedal torque, this crankset comprising a pedal crank that rotates about a crank spindle; - an electric motor comprising a stator and a rotor that can rotate about a rotor spindle; - a first torque transmission mechanism, the first mechanism comprising a first input wheel that can be driven in rotation about the crank spindle, a first flexible transmission element, at least one first output wheel that can be driven by the first input wheel by the first flexible element, a freewheel device that is designed to transmit the pedal torque to the rear wheel via the first output wheel; - a second torque transmission mechanism which is distinct from the first mechanism, the second mechanism comprising a second input wheel that can be driven in rotation about the spindle of the rotor, a second flexible transmission element, at least one second output wheel that can be driven by the second input wheel via the second flexible element, a second freewheel device that is designed to transmit the motor torque to the rear wheel via the second output wheel; - the electric motor, its electrical power storage system and its control electronics and the second torque transmission mechanism being configured to directly transmit the torque from the motor to the rear wheel with no pedal torque, even when starting the bicycle from rest; characterized in that the spindle of the rotor is spaced apart from while still being close to the pedal crank, and in that the second freewheel device is housed in a support assembly forming a two-part housing of which the fixed part is attached on one hand to the rear wheel axle by means of a connecting part attached to the hub, and on the other hand to a brake disk of the rear wheel, while the movable part is attached to the second output wheel, being secured to the outside of the second freewheel device. - a rear wheel provided with a wheel axle mounted in a hub; - a rear portion of the frame having two seat stays (20, 21) that are spaced apart from one another so as to define the space for receiving the rear wheel; - a crankset that is designed to be actuated by the muscular force of a user in order to transform that force into a pedal torque, this crankset comprising a pedal crank that rotates about a crank spindle; - an electric motor comprising a stator and a rotor that can rotate about a rotor spindle; - a first torque transmission mechanism, the first mechanism comprising a first input wheel that can be driven in rotation about the crank spindle, a first flexible transmission element, at least one first output wheel that can be driven by the first input wheel by the first flexible element, a freewheel device that is designed to transmit the pedal torque to the rear wheel via the first output wheel; - a second torque transmission mechanism which is distinct from the first mechanism, the second mechanism comprising a second input wheel that can be driven in rotation about the spindle of the rotor, a second flexible transmission element, at least one second output wheel that can be driven by the second input wheel via the second flexible element, a second freewheel device that is designed to transmit the motor torque to the rear wheel via the second output wheel; - the electric motor, its electrical power storage system and its control electronics and the second torque transmission mechanism being configured to directly transmit the torque from the motor to the rear wheel with no pedal torque, even when starting the bicycle from rest;