An element comprises a rotary input member (15), a motion output member (19), an electrical machine (14) including a stator (27) and a rotor (26), a first connecting clutch (89A) between the input member (15) and an intermediate member (83) rotating about a first axis (X-X′). The intermediate member (83) is connected in rotation to the rotor (26), and a second connecting clutch (89B) is positioned between the intermediate member (83) and the output member (19). The element also comprises a casing (21) defining a housing (69) wherein are coaxially and concentrically mounted the first and second connecting clutches (89A, 89B). The axis of rotation (Y-Y′) of the rotor (26) is separate from the first axis (X-X′) and a transmission (121, 123, 135) connects in rotation the rotor (26) and the intermediate member (83). The invention is applicable to motor vehicle engine-transmission units.