  General expressions for quantum electrodynamic corrections to the one-loop
self-energy [of order alpha(Zalpha)^6] and for the two-loop Lamb shift [of
order alpha^2(Z\alpha)^] are derived. The latter includes all diagrams with
closed fermion loops. The general results are valid for arbitrary excited non-S
hydrogenic states and for the normalized Lamb shift difference of S states,
defined as Delta_n = n^3 DeltaE(nS) - DeltaE(1S). We present numerical results
for one-loop and two-loop corrections for excited S, P and D states. In
particular, the normalized Lamb shift difference of S states is calculated with
an uncertainty of order 0.1 kHz.
