Headrest for a motor vehicle seat, said headrest comprising: - a metal connection framework at the back of said seat, - a case made of moulded plastic material for absorbing energy in case of an impact of the head of a passenger on said headrest, said case being associated to said framework in a fixed manner in a longitudinal direction, - a movable portion mounted at the front of said case in such a way as to be able to be displaced longitudinally, said portion being provided with a front wall for receiving a headrest cushion, - a device for adjusting the longitudinal position of said portion with respect to said case, in such a way as to allow for a longitudinal adjustment of said cushion, said device comprising: - - an electric motor mounted integrally with said case, - - a threaded rod extending longitudinally, said rod being rotatably mounted in said case in cooperation with said motor in such a way as to be rotated in one direction or in the other by actuation of said motor in one direction or in the other, - - a means of receiving said rod through a threaded orifice provided in said means, said means being fixed at the rear of said wall via a spacer member shifting it towards the rear with respect to said wall over a distance substantially equal to the length of said rod, said headrest being characterised in that said motor is disposed laterally with respect to said rod, in such a way as to not substantially extend to the front nor the rear of said rod. - a metal connection framework at the back of said seat, - a case made of moulded plastic material for absorbing energy in case of an impact of the head of a passenger on said headrest, said case being associated to said framework in a fixed manner in a longitudinal direction, - a movable portion mounted at the front of said case in such a way as to be able to be displaced longitudinally, said portion being provided with a front wall for receiving a headrest cushion, - a device for adjusting the longitudinal position of said portion with respect to said case, in such a way as to allow for a longitudinal adjustment of said cushion, said device comprising: - - an electric motor mounted integrally with said case, - - a threaded rod extending longitudinally, said rod being rotatably mounted in said case in cooperation with said motor in such a way as to be rotated in one direction or in the other by actuation of said motor in one direction or in the other, - - a means of receiving said rod through a threaded orifice provided in said means, said means being fixed at the rear of said wall via a spacer member shifting it towards the rear with respect to said wall over a distance substantially equal to the length of said rod, - - an electric motor mounted integrally with said case, - - a threaded rod extending longitudinally, said rod being rotatably mounted in said case in cooperation with said motor in such a way as to be rotated in one direction or in the other by actuation of said motor in one direction or in the other, - - a means of receiving said rod through a threaded orifice provided in said means, said means being fixed at the rear of said wall via a spacer member shifting it towards the rear with respect to said wall over a distance substantially equal to the length of said rod, <EOS>