A kinetic approach that takes account of reactions with neutrons, prot
ons, and alpha-particles, as well as beta-decay, is proposed to study
nucleosynthesis. As a test problem, this approach is applied to rapid-
nucleosynthesis calculations for different model conditions, making it
possible to avoid a number of simplifications commonly used to calcul
ate the r-process. The reasons for the appearance and smoothing of an
odd effect in the calculated abundance curve are analyzed. Conditions
under which the results of calculations depend only weakly on the meth
od of representing the neutron cross-sections are determined, allowing
the requirements on the quality of the neutron data to be relaxed at
high temperatures and neutron densities. Our calculations for differen
t conditions lead us to conclude that the boundary conditions play a c
rucial role in forming the structure of the abundance curve. It is sho
wn that under certain conditions, all r-elements beyond the iron peak
can be produced during a single astrophysical event in the presence of
a neutron source and seed nuclei. A number of original algorithms are
used to perform the calculations.