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This paper describes two hybrid methods coupling finite formulation of electromagnetic fields (FFEF) in a bounded domain to integral boundary conditions taking into account far field conditions. The two hybrid techniques use different boundary conditions: the first formulation is based on Green's function applied to magnetization source inside bounded domain while the other one is based on a boundary-element method on its external surface. Details about the coupling terms are given and handling of different magnetization sources is described, including the fictitious magnetization sources coming from nonlinear solutions. The proposed methods are validated versus different benchmark cases. Comparisons between the two techniques have been performed using different criteria (accuracy and convergence, memory requirements, etc.).