[en] The theory of S-process heavy-element formation is reformulated to allow for competition between beta decay and neutron capture at various nuclei along the path. Solutions to the resulting branching network equations are presented (under the assumption of constant temperature and neutron flux) that do not require steady flow for the neutron current. Using the exponential exposure distribution rho (tau) =G exp(-tau/tau₀) and recently calculated temperature-dependent beta-decay rates, comparison of several key branches yields the following average conditions for the solar-system S-process environment: Tapprox. =3.1 x 10⁸ K, n/subn/approx. =1.6 x 10⁷ neutrons cm^-3. For tau₀=0.25 n mb^-1 we find that about 4.8 neutron captures per exposed iron seed are required over a time of the order of a few thousand years for synthesis of the bulk of the solarsystem S-process material, with an average neutron capture time approx.10 years (for sigmaapprox.500 mb)