Full transport solutions of time-dependent problems can be computationally very expensive. Therefore, considerable effort has been devoted to developing approximate solution techniques that are much faster computationally and yet are accurate enough for a particular application. Many of these approximate solutions have been used in isolated problems and have not been compared to each other. This paper presents two test problems that test and compare several approximate transport techniques. In addition to the diffusion and P 1 approximations, we will test several different flux-limited diffusion theories and variable Eddington factor closures. For completeness, we will show some variations that have not yet appeared in the literature that have some interesting consequences. For example, we have found a trivial way to modify the P 1 equations to get the correct propagation velocity of a radiation front in the optically thin limit without modifying the accuracy of the solution in the optically thick limit. Also, we will demonstrate nonphysical behavior in some published techniques.