Using a new diagram technique for the Anderson—Newns model, the expression for the self-energy in the second order in the rebonding interaction is obtained for arbitrary values of the Fermi energy of a metal. The approximate expression for the self-energy beyond the second order is also suggested for H chemisorbed on narrow-band transition metals. The adatom densities of states are calculated for the sets of parameters, imitating hydrogen chemisorption on Ni and Pd. The results are compared with the measured photoemission and inverse photoemission spectra and other theoretical results in the literature. The influence of many-body effects on the positions of the discrete levels, their widths or weights and on the existence of the continuous bands of the adatom density of states is discussed. It is shown that many-body effects are important for H chemisorbed on narrow-band transition metals with almost-filled d bands.