Silicon carbide semiconductor radiation detectors are resistant to radiation induced damage and can be operated at elevated and changing temperatures., Silicon carbide radiation detectors have been shown to have linear responses to both neutrons and gamma rays. Furthermore, these responses are separable on the basis of pulse height, making simultaneous monitoring of both neutrons and gamma rays possible. The neutron and gamma ray sensitivities of silicon carbide radiation detectors are well-matched to the radiation environments characteristic of spent nuclear fuel. Measurements have been carried out in mixed gamma/neutron fields in a hot cell and at a reactor facility under conditions chosen to approximate the radiation fields typically encountered in the vicinity of spent nuclear fuel assemblies. The results of these measurements and the application of silicon carbide radiation detectors to spent fuel dosimetry are discussed.