The theory of the s process of nucleosynthesis has received considerable development during recent years, mainly as the result of more detailed physical and mathematical treatments and also as a result of the accumulation of new observational data on stellar evolution and the abundance of the elements in the solar system, and accumulation of experimental data on neutron-capture cross sections. The exact solution of the sprocess equations obtained recently by Newman (1978) is discussed. It confirms the correctness of the initial sprocess theory (Clayton, Fowler, Hull, and Zimmerman, 1961). At the same time for small neutron exposures the exact and initial solutions differ. The influence of branching of the s-process due to competition between $\beta$ decay and neutron capture is analyzed; it is noted that at a temperature $\sim$3 $\cdot$ 10$^8$ K and a density of free neutrons 1,6 $\cdot$ 10$^7$ cm$^{-3}$ the s-process theory is in good agreement with observational data on the yields of the various nuclides. Models are discussed for the pulsed neutron s process, which leads to formation of heavy elements in the interior of a star as the result of periodic flares of the helium shell and subsequent remixing of the material.