Convergence problems on the fully-coupled calculation of strongly radiating hypersonic flowfields are discussed. Calculations are conducted for the inviscid flow over an axisymmetric blunt body of 1.5m nose radius. The case of the flow Mach number 46.8 is considered. Radiative transfer equation is solved using a model developed earlier which combines Planck, Rosseland and Gray-gas models. The radiative heat flux is calculated two-dimensionally. In the calculation, the governing equations are integrated in time implicitly, but the radiative source term is treated explicitly. It is shown that converged solution can be obtained for strongly radiating flowfield with considerably large CFL numbers even if the radiative source terms are integrated explicitly.