The flow field within an axial flow turbomachine, such as a turbine or compressor, is extremely complex because of three-dimensional features such as hub-corner-stall, tip leakage flows, and airfoil wakes. These flow features interact with each other and with rotor and stator airfoils inducing time-varying forces on the airfoils. These complicated rotor/stator interactions must be understood in order to design turbomachines that are light and compact as well as reliable and efficient. Two codes, STAGE-2 and STAGE-3, have been developed to compute these unsteady rotor/stator interaction flows in multistage turbomachines. An implicit, thin-layer Euler/Navier-Stokes zonal algorithm is used to compute the unsteady flowfield within both turbine and compressor configurations. Results include surface pressures and wake profiles for two-dimensional turbine and compressor configurations and surface pressures for a three-dimensional single-stage turbine configuration. The results compare well with experimental data and other unsteady computations.