A microwave device for de-icing and keeping areas of hollow body structures free from ice keeps atmospherically flown-against edges and linear areas emanating therefrom by means of a coolant circuit. The surface segments between the linear areas are kept free from ice as a result of the effect of said microwave device upon the wall of said surface segments and the heating that ensues following coupling by de-icing the boundary layer between the ice and the surface. A series of consecutive microwave-tight chambers is disposed behind the wall of the area which is flown against. A microwave source respectively feeds into said chambers with the aid of a decoupling structure fitted therein, resulting in high/multimode excitation. The lost heat from the microwave sources is collected by means of a coolant circuit and double lines in the edge and transported to the linear areas emanating therefrom for permanent heating in order to keep the ice away. The microwave sources are operated in cycles.