Analytical expressions for the spatially independent spectrum and importance (adjoint) function in fast-reactor assemblies have been developed. These expressions were obtained by solving the neutron balance equation, and the equation adjoint thereto, by the method of successive approximation. Solutions obtained in this manner suggest an interpretation of the collision density in terms of the probability that a fission neutron suffers a given sequence of scattering collisions, summed over all such sequences. Similarly, the importance function is interpreted in terms of the fission-neutron production probability following a given sequence of scattering collisions, summed over all such sequences. The analytical expressions are readily evaluated using either differential or group-averaged cross-section values. Integral properties of highly enriched and dilute fast-reactor assemblies were evaluated and compared with experiment; the agreement was comparable with that obtained with multigroup calculations normally employed to evaluate such assemblies.