Yes, the Gigaset Comfort 550 HX can be connected to a Swisscom Internet Box 4 that is connected to a digital home connection. The device is compatible with all DECT/CAT-iq-enabled routers, and the Swisscom Internet Box 4 supports this technology. It can be easily connected to routers such as the FRITZBox or the Telekom Speedport, which also applies to the Swisscom Internet Box 4.