Hall’s differential operator method for the Monte Carlo calculation of sensitivities was extended so as to apply to point-detector-type problems. By this method, the evaluation of the sensitivities of the detector response (or, equivalently, those of the neutron flux at the detector) to material parameters of interest (cross sections, average number of fission neutrons, number densities) is concurrent with that of the very response. In such a Monte Carlo game, the neutron histories, or paths, are sampled, collision by collision, and the calculated contributions of each collision to the response and to its partial derivatives with respect to the parameters of interest are accumulated. For each path, these sums are the estimates for the response and its respective sensitivities. The Monte Carlo evaluations are then the respective averages of the individual path estimates. This procedure was applied to the analysis of the time-of-flight spectra of the leakage from several of the Livermore pulsed spheres. As an illustration, measured and calculated spectra and some calculated sensitivities are depicted and discussed.