The fragmentation of molten cladding films into rivulets and single waves is investigated. This problem is especially relevant to liquid-metal fast breeder reactor safety analysis because of its impact on the flow regime of the clad melt. Among other effects, various instabilities may contribute to film breakup. In the axial direction, the Kelvin-Helmholtz instability can arise. As the Sandia transient axial relocation experiments frequently exhibit, an azimuthal fragmentation process also occurs. Consequently, another instability due to thermocapillarity is proposed.