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Higher order nonreflecting blade row interfaces are today widely used for performing both steady and unsteady simulations of the flow within axial turbomachines. In this paper, a quasi-three-dimensional nonreflecting interface based on the exact, two-dimensional nonreflecting boundary condition for a single frequency and azimuthal wave number developed by Giles is presented. The formulation has been implemented to work for both steady simulations as well as unsteady simulations employing the nonlinear Harmonic Balance method. The theory behind the construction of the nonreflecting interface is presented and details on the numerical implementation is also provided. The implementation is verified for two dimensional wave propagation along a straight cascade. It is shown that the interface correctly absorbs incoming waves, but also found that the chosen implementation strategy may be ill-posed. A simple solution to stabilize the implementation is therefore implemented, but future work should seek a more generic solution to this problem.