Adaptive remeshing schemes for transient problems are presented. The main advantage of these schemes is the ease in incorporating directional refinement and body motion in the context of adaptive refinement. Practical numerical examples for the Euler equations, run on the CRAY-XMP-24 at NRL, show that the adaptive remeshing scheme by itself cannot compete with ordinary h-refinement for strongly unsteady flows that require a grid change every 5–10 timesteps. Therefore, we study the combination of adaptive remeshing and h-refinement. After generating a coarser grid with stretched elements, the whole grid is h-refined at once. Even with one level of h-refinement, the combined scheme easily out-performs ordinary h-refinement, yielding a very effective adaptive refinement method for this class of problems.