Analytical exploratory investigations indicate that transition effects such as streaming cause a considerable spatial variation in the neutron spectra across resonances; streaming leads to opposite effects in the forward and backward directions. The neglect of this coupled spatial/angular variation of the transitory resonance spectra is an approximation that is common to all current group constant generation methodologies. This paper aims at an accurate description of the spatial/angular coupling of the neutron flux across isolated resonances. It appears to be necessary to differentiate between forward- and backward-directed neutron flux components or even to consider components in narrower angular cones. The effects are illustrated for an isolated actinide resonance in a simplified fast reactor blanket problem. The resonance spectra of the directional flux components φ+ and φ‾, and even more so the 90-deg cone components, are shown to deviate significantly from the infinite medium approximation, and the differences increase with penetration. The changes in φ+ lead to a decreasing scattering group constant that enhances neutron transmission; the changes in φ‾ lead to an increasing group constant inhibiting backward scattering. Therefore, the changes in the forward- and backward-directed spectra both lead to increased neutron transmission. Conversely, the flux (φ = φ + + φ‾) is shown to agree closely with the infinite medium approximation both in the analytical formulas and in the numerical solution. The directional effects cancel in the summation. Therefore, flux-weighted (“diffusion theory”) group constants cannot accurately describe the transmission problem, even using transport theory, as the use of flux weighting eliminates the significant directional effects. The forward- and backward-directed flux components are used as weighting spectra to illustrate the group constant changes for a single resonance. Results indicate that these changes have a magnitude that can likely account for calculational underpredictions observed in fast reactor blanket regions.