An exhaust-gas cooling device for an internal combustion engine includes a housing with an exhaust-gas inlet, an exhaust-gas outlet, a valve device, and a U-shaped heat exchange unit including an outbound flow path and a return flow path. The housing comprises, on the open side of the U-shaped heat exchange unit, a first, a second and a third chamber. The first chamber provides a fluid connection from the exhaust-gas inlet to the second chamber, and the third chamber provides a fluid connection from the second chamber to the exhaust-gas outlet. The valve device is arranged in the second chamber such that the second chamber can be divided into two partial chambers, a first one of the partial chambers is arranged in fluid connection with the outbound flow path, and the second one of the partial chambers is arranged in fluid connection with the return flow path.