A rocking device provided with a fastening means (9) for mounting to for example a baby buggy to create an automatic rocking movement of the baby buggy. It comprises a rotating, asymmetrical weight (14) driven by an electric moto (24). The motor and weight are suspended in a rigid fastening bracket. The fastening bracket (13) is fastened to a first side of a vibration dampening connection element (3) of an at least partly soft material. The fastening means is fastened to the other side of the vibration dampening connection element (3), such that the movement of the weight is transmitted through the fastening bracket (13), via the vibration dampening connection element (3) and the fastening device, to the baby buggy. The fastening bracket with motor a weight is enclosed by an outer cover (1, 2) which is not in contact with the fastening bracket, motor or weight. The outer cover is fastened to the vibration dampening connection element (3), such that vibrations from the motor and the weight are not transmitted to the outer cover.