Rocking device for a stroller (2), including at least one main element (10) provided with a motor (40) and rolling means (21, 23) on its lower face, the motor and the rolling means being designed to drive the main element in a back and forth movement, the upper face of the main element (10) being designed to take a wheel (3) or (4) of the stroller. The rolling means are designed to roll on the ground and the device comprises a means for automatically starting the back and forth movement as a result of a deliberate action on the part of the user in pushing the stroller (2) so as to drive the main element (10) at least once in a first direction and at least once in the direction opposite to the first direction.