The time-dependent polarized fluorescence and optical density transients arising from electronic excitation transport are derived for solutions of randomly oriented chromoproteins in which the chromophore transition moments have well-defined orientations with respect to the protein. The treatment is extended to oriented monolayers of chromoproteins, in which the molecules are aligned with a particular protein-fixed axis perpendicular to the surface plane and with random azimuthal angles about the surface normal. The initial ratio of parallel to perpendicular transients is invariably 3 : 1, irrespective of system dimensionality and chromophore organization. The residual anisotropy observed at long times is directly related to the relative orientations of the donor and acceptor chromophores. These calculations form a basis for detailed interpretation of ultrafast fluorescence and pump-probe linear dichroism studies in photosynthetic systems, for which 3-dimensional structures are becoming increasingly available.