Passage vortical flows, endwall boundary layers, tip leakage flows and airfoil wakes combine to form the three-dimensional flowfields found in axial turbomachines. In addition, turbomachinery flow fields are also inherently unsteady because of the relative motion between rotor and stator airfoils. This relative motion causes complex, time-varying aerodynamic interactions to occur between the different aerodynamic structures and the rotor and stator airfoils. It is necessary to understand the three-dimensional, unsteady 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 a time-accurate, three-dimensional, thin-layer Navier-Stokes zonal approach to investigate the unsteady aerodynamics of multistage axial turbomachines. Relative motion between rotor and stator airfoils is accounted for by the use of systems of patched and overlaid grids. Time-averaged surface pressures, surface flow visualizations and time-averaged flow field contours have been computed for a - stage turbine and are in good agreement with experimental data. This favorable comparison represents a validation of the current method for unsteady computations of multistage turbomachinery flows.