In this paper we calculate the energy distribution for six cases of Vaidya-type solutions in the Møller prescription. With the exception of the energy complex of Møller for the monopole solution which vanishes everywhere, the other solutions have a non-zero energy component. Only the energy distributions of the de Sitter and anti-de Sitter solution are independent of the advanced/retarded time v. For the radiating dyon solution, the difference in the energy complex between Møller's and Einstein’s prescription is just like the case for the Reissner-Nordstr¨om solution.