There exists an inverse relationship between the relative abundance of nuclear species in the universe and the neutron-capture cross sections of these nuclei. Abundant nuclei have small capture cross sections, and vice versa. On the basis of this correlation, a non-equilibrium theory of the formation of the elements is developed in which the elements are built up by a process of successive neutron captures. The coefficients in the equations of this theory involve the neutron-capture cross sections of the elements, and for this reason relationships between capture cross sections, atomic weights, and neutron energies are obtained from available data. According to this theory, the primordial material was a gas of neutrons only. As the universe expanded, neutrons decayed to protons and electrons; the capture of neutrons by protons then led to deuterons. These nuclei in turn captured neutrons, and progressively heavier nuclei were formed. The neutron content in these nuclei was controlled by beta-decay between successive neutron captures. The physical conditions which are indicated for the period of element formation are inconsistent with a cosmological model of the early stages of the universe based on matter only. It appears that the early stage was probably a universe of radiation with a trace of matter present. According to this picture, the element-building process began some 200 to 300 seconds after the start of the expansion, at which time the temperature was of the order of 109°K, and the density of matter was of the order of 10-3 g/cm3. Because of the expansion of the universe, and because of the decay of neutrons, the production of elements must have been essentially complete in a time of the order of magnitude of the neutron decay lifetime. Preliminary calculations based on this theory successfully predict the observed relative abundance data.