The phenomenological description of transport processes in a fluid composed of molecules or particles which are orientable is reformulated so as to render it capable of distinguishing between and determining the form of the distribution of orientation. With orientation variables playing the role of continuously distributed parameters suitable for tensorial labeling of multicomponent species, equations for the transport of mass, momentum, energy, and angular momentum in the position‐orientation hyperspace are independently derived by continuum and statistical mechanical arguments. The selection of the point of location of a particle is shown to have an important bearing upon the transport equations of physical space obtained by orientation averaging. Linear constitutive relations are established by means of thermodynamic arguments which suggest anisotropic thermal conductivity and viscosity as well as a coupling tensor each dependent for its anisotropy upon the polyadic (polarization) moments of the distributions. The rotational and translational diffusion fluxes are predicted to be governed by rotational, translational, and coupling multicomponent diffusion tensors, thermal diffusion tensors, and by the analogous shear diffusion tensors. The special case of dilute solution theory is examined and the thermodynamic predictions of generalized transport laws reaffirmed by appeal to component (orientation specific) balances of linear and angular momentum.