A procedure for measuring neutron cross sections and their ratios based on the multiplicity spectrometry of gamma quanta and neutrons emitted by excited nuclei is considered. Multiplicity spectrometers are described, and their functional characteristics are presented. Results of the radiative capture of fissile nuclei and highly precise alpha value measurements are analyzed in detail. Certain results of the absolute alpha value measurement at 235U resonances over the energy range up to 35 eV are given. The accuracy of the data obtained is ∼2%.