The purpose of the present paper is to propose a higher-resolution numerical method for simulating unsteady subsonic and transonic viscous flows in wet or steam condition. The fundamental equations contain the compressible Navier-Stokes equations and the model equations for vapor and liquid phases. The classical condensation theory is implemented to model the nonequilibrium condensation. These equations are solved using the fourth-order accurate compact MUSCL TVD scheme and the maximum second-order implicit scheme. As numerical examples, unsteady transonic viscous flows around the 2-D airfoil in atmospheric wind tunnel conditions are first calculated. The present method is also applied to the calculation of unsteady turbine stator-rotor interactions in wet-steam condition.