**Abstract** : Electro-magneto-optical effects in stationary materials are observed when the materials are placed in strong, static electric or magnetic fields and an electromagnetic wave (light) traverses the medium. The Faraday effect is an example of the class of phenomena we have in mind. Clearly, the existence of electromagneto- optical effects in material media is direct evidence that the equations for the electromagnetic field in a material medium, unlike the equations for it in vacuum, are non-linear since the sum of two solutions generally fails to be a solution. An analysis of electro-magneto-optical effects, though based on nonlinear equations for which all but the simplest exact solutions are difficult to exhibit, may be simplified and made tractable by assuming that the dynamical part of the solution (the light wave) has such weak intensity that the vectors which describe it may be treated as infinitesimals. Accordingly, in this paper we assume that the electric displacement and magnetic intensity fields are functions of the static electric and magnetic induction fields and linear functionals of the small dynamical electric and magnetic induction fields. This starting point is derived, in the Appendix, from the assumption that for a more general class of fields, not necessarily representable as the superposition of small dynamic fields on large static fields, the electric displacement and magnetic intensity fields are non-linear functionals of the electric and magnetic induction fields. From our initial assumption regarding the variables which enter into the constitutive equations, we derive the limitations which are imposed on them by the assumption that the material is isotropic. The isotropic constitutive equations are then applied to the study of the manner in which a plane electromagnetic wave is propagated in an isotropic material to which static electric and magnetic induction fields are simultaneously applied. From these results we consider in greater detail the cases when the applied electric field is zero, leading to the magneto-optical effects, and that when the applied magnetic induction field is zero, leading to the electro-optical effects. The case when both the static electric and magnetic induction fields are nonzero will be given more detailed consideration in a later paper.