Fluid dynamics of turbomachines are complicated because of aerodynamic interactions between rotors and stators. It is necessary to understand the aerodynamics associated with these interactions in order to design turbomachines that are both light and compact as well as reliable and efficient. The current study uses an unsteady, thin-layer Navier-Stokes zonal approach to investigate the unsteady aerodynamics of a multistage compressor. Relative motion between rotors and stators is made possible by the use of systems of patched and overlaid grids. Results have been computed for a þstage compressor configuration. The numerical data compare well with experimental data for surface pressures and wakes. In addition, the effect of grid refinement on the solution is studied.