The concept of a transfer function for a nuclear system is extended to include spatial effects. The general equation is derived using the time-dependent Fermi age and diffusion theories for a single-region, isotropic, homogeneous medium. The fluctuations of the thermal-neutron density at any point in the assembly is related to the variation of the fast-neutron source. The general transfer function equation is specialized for several cases, including the case of a point source in a cylindrical medium. Theoretical curves are calculated for multiplying and non-multiplying media and compared with the commonly used lumped-parameter transfer function. The results indicate, in general, that the lumped-parameter model predicts the correct behavior of the nuclear system only if the output detector is carefully positioned at a specific distance from the source. If the detector is located elsewhere, the lumped-parameter model is not capable of accurate results. The theoretical equations were used to calculate the spatially dependent transfer function between two detectors (the cross-transfer function) that were located within light- and heavy-water subcritical assemblies, simulating some experimental measurements. A comparison of the experimental and theoretical transfer functions indicate that the Fermi age, diffusion theory model might be quite adequate in describing the kinetics of a nuclear system.