  QED theory of multiphoton cascade transitions in atoms and ions is developed.
This theory allows for the accurate description of the process important for
astrophysical studies of the cosmological hydrogen recombination. In particular
the $ 3s\rightarrow1s+2\gamma $, $ 4s\rightarrow1s+2\gamma $ and $
3p\rightarrow1s+3\gamma $ processes are considered and some controversies
existing in the literature are resolved.
