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The three-dimensional Gaussian beam transmission through a ferrite-semiconductor finely-stratified structure being under an action of an external static magnetic field in the Faraday geometry is considered. The beam field is represented by an angular continuous spectrum of plane waves. In the long-wavelength limit, the studied structure is described as a gyroelectromagnetic me-dium defined by the effective permittivity and effective permeability tensors. The investigations are carried out in the frequency band where the real parts of the on-diagonal elements of both effective permittivity and effective permeability tensors are close to zero while the off-diagonal ones are non-zero. In this frequency band the studied structure is referred to a gyrotropic-nihility medium. It is found out that a Gaussian beam keeps its parameters unchanged (beam width and shape) when passing through the layer of such a medium except of a portion of the absorbed energy.