Baby rocking device adapted to impart a reciprocating cycling rocking movement to a perambulator, push-chair or the like, in which said baby rocking device comprises: - at least one receiving and supporting member configured for receiving and supporting at least one element, such as a wheel, of the perambulator or push-chair, and - an actuation member for causing a cyclic reciprocating movement of said at least one receiving and supporting member on a floor, said baby rocking device being characterized in that said actuation member is constituted by a single roller having an electric motor arranged inside the roller and configured for rolling on the floor alternately in two opposite directions, said single roller including: - an inner non-rotating core , having two end portions projecting from opposite ends of the roller and connected to two receiving and supporting members configured for receiving two respective wheels of the perambulator or push-chair, in such a way that the perambulator or push-chair is placed astride said single roller , and - an outer cylindrical shell for contact with the floor, which is rotatably mounted on said inner core , - said electric motor being carried by said inner core and being configured for actuating the rotation of said outer shell alternately in two opposite directions of rotation, so as to cause the rolling of said single roller on the floor, alternately in two opposite directions. - at least one receiving and supporting member configured for receiving and supporting at least one element, such as a wheel, of the perambulator or push-chair, and - an actuation member for causing a cyclic reciprocating movement of said at least one receiving and supporting member on a floor, said baby rocking device being characterized in that said actuation member is constituted by a single roller having an electric motor arranged inside the roller and configured for rolling on the floor alternately in two opposite directions, said single roller including: - an inner non-rotating core , having two end portions projecting from opposite ends of the roller and connected to two receiving and supporting members configured for receiving two respective wheels of the perambulator or push-chair, in such a way that the perambulator or push-chair is placed astride said single roller , and - an outer cylindrical shell for contact with the floor, which is rotatably mounted on said inner core , - said electric motor being carried by said inner core and being configured for actuating the rotation of said outer shell alternately in two opposite directions of rotation, so as to cause the rolling of said single roller on the floor, alternately in two opposite directions. - an inner non-rotating core , having two end portions projecting from opposite ends of the roller and connected to two receiving and supporting members configured for receiving two respective wheels of the perambulator or push-chair, in such a way that the perambulator or push-chair is placed astride said single roller , and - an outer cylindrical shell for contact with the floor, which is rotatably mounted on said inner core , - said electric motor being carried by said inner core and being configured for actuating the rotation of said outer shell alternately in two opposite directions of rotation, so as to cause the rolling of said single roller on the floor, alternately in two opposite directions. <EOS>