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A set of electromagnetic boundary conditions requiring vanishing of the normal components of the D and B fields (DB boundary) or their normal derivatives (D'B' boundary) have been recently under interest. In the present study, more general conditions called those of the generalized DB boundary (GDB boundary) are introduced. The boundary depends on a parameter (GDB parameter) whose two special values yield the DB and D'B' boundaries. It is shown that, for the plane-wave reflection of a planar GDB boundary, the boundary can be replaced by an anisotropic impedance boundary with impedance dyadic depending on the direction of propagation of the plane wave. Numerical analysis of a sphere with GDB boundary shows that it yields a wide backscattering zero for an incident plane wave, while its forward scattering magnitude depends on the GDB parameter. Finally, yet another set of generalized boundary conditions is introduced that corresponds to that of an isotropic impedance boundary while being represented in terms of normal field quantities.