This paper describes the procedure to predict steady and unsteady performances of a contrarotating propeller(CRP) by a mixed formulation of the boundary value problem(BVP) far the flow around a CRP. The blade BVP is treated by a classical vortex lattice method, whereas the hub BVP is solved by a potential-based panel method. Blades and trailing wakes are represented by a vortex and/or source lattice system, and hubs are represented by normal dipole and source distributions. Both forward and aft propellers are solved simultaneously, thus treating the interaction effect without iteration. The unsteady performance is computed directly in time domain. The new numerical procedure requires a large amount of storage and computing time, which is however no longer a limit in a modern computer system. Sample computations show that the steady performance compares very well with the experiments. The predicted unsteady behavior shows that the dominant harmonics of the total forces are multiples of not only the number of blades of the forward and aft propellers but also the product of both blade numbers. The magnitude of the latter harmonics, present also in uniform oncoming flow, may reach abort 50% of the mean torque for the aft propeller, which in turn may cause a serious vibration problem in the complicated contrarotating shafting system.