A propulsion and motion-transmission assembly (1), in particular for a rotary-wing aircraft, the assembly (1) comprising:--a first hydrostatic transmission (2) including a first fluid machine for converting mechanical energy into fluid energy (18) and a first fluid machine for converting fluid energy into mechanical energy (26);--a second hydrostatic transmission (8) including a second fluid machine for converting mechanical energy into fluid energy (62) and a second fluid machine for converting fluid energy into mechanical energy (70); and wherein each of said first and second hydrostatic transmissions (2, 8) comprises a high-pressure branch (24, 68) and a low-pressure branch (30, 74), which, in each of said first and second hydrostatic transmissions (2, 8), hydraulically connect the fluid machine. The assembly (1) further comprises valve means (108, 112) that can be actuated for enabling a first hydraulic connection (106) between the low-pressure branch (30) of the first hydrostatic transmission (2) and the low-pressure branch (74) of the second hydrostatic transmission (8).