[en] This paper gives a systematic treatment for a non-stationary radiation diffusion problem which involves a coupled system of integro-differential equations and some initial and boundary conditions. Using an iterative scheme the author obtains a recursion formula for the calculation of approximate solutions as well as their error estimates. It is shown that the sequence of approximations converges to a unique classical solution which also leads to an existence-uniqueness theorem. In addition, it is shown that the solution is positive and depends continuously on the external source and the initial-boundary data. The latter property together with the existence-uniqueness theorem insure that the system is well-posed in the sense of Hadamard. (Auth.)