  Contributions to HFS and to the Lamb shift intervals of order
$\alpha^2(Z\alpha)^5$ induced by graphs with two radiative photons inserted in
the electron line are considered. It is demonstrated that this last gauge
invariant set of diagrams which are capable of producing corrections of
considered order consists of nineteen topologically different diagrams.
Contributions both to HFS and Lamb shift induced by graphs containing one-loop
electron self-energy as a subgraph and also by the graph containing two
one-loop vertices are obtained.
