The late-time (t ≥ 80 ns) behaviour of hohlraums designed for the National Ignition Facility (NIF) is simulated using the multiphysics radiation hydrodynamics codes LASNEX and HYDRA. The spatial distribution of x-radiation outside the hohlraum is shown as a function of time. The energy spectrum of the x-ray emission is presented for various hohlraum viewing angles. We have made refinements to the grid motion algorithms in the arbitrary Lagrangian Eulerian (ALE) hydrodynamics code HYDRA to obtain the first late-time simulations of a hohlraum that can be used to give the spatial distribution of the vaporized hohlraum wall. The importance of late-time simulations in determining the lifetimes of debris shields on NIF is discussed.