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The Maxwell equations and the constitutive relations describe the classical propagation of electromagnetic waves in continuous matter. Here, we investigate the effects stemming from extended constitutive relations on the propagation of waves in bi-isotropic and bi-anisotropic media using a classical general approach based on the evaluation of dispersion relations and refractive indices. For the bi-anisotropic media, we specify two classes of magnetoelectric parameters represented by symmetric and antisymmetric tensors. The three cases examined have provided real and distinct refractive indices for two propagating modes, which implies birefringence. The propagating modes were also carried out in all cases. The anisotropy or birefringence effect, given by the rotatory power or phase difference, was evaluated in terms of the magnetoelectric parameters of the theory in each case. The propagation orthogonal to the vectors used to parametrize the symmetric and antisymmetric magnetoelectric tensors is described by distinct modes, representing a route to identify the kind of bi-anisotropic medium examined. The group velocity and Poynting vector were also evaluated for all the cases examined to discuss the energy propagation in these anisotropic media.