Summary: The nonaligned multigrid method is introduced as an alternative to boundary point interpolation for communication in overset grid systems. The nonaligned multigrid method treats the individual grids as levels in a multigrid solution procedure. This technique was able to converge 69\% faster than standard boundary point interpolation for Mach 2 flow over a 5-deg ramp and 28\% faster for a more complex reflected shock case. For these test cases, the largest increase in convergence rate came from applying the nonaligned multigrid method to the communication between overset grids. Further coarsening of the global grid was next in effectiveness, and coarsening of local grids gave little improvement.