  Two-loop Bethe logarithms are calculated for excited P and D states in
hydrogenlike systems, and estimates are presented for all states with higher
angular momenta. These results complete our knowledge of the P and D energy
levels in hydrogen at the order of alpha^8 m_e c^2, where m_e is the electron
mass and c is the speed of light, and scale as Z^6, where Z is the nuclear
charge number. Our analytic and numerical calculations are consistent with the
complete absence of logarithmic terms of order (alpha/pi)^2 (Z alpha)^6 ln[(Z
alpha)^(-2)] m_e c^2 for D states and all states with higher angular momenta.
For higher excited P and D states, a number of poles from lower-lying levels
have to subtracted in the numerical evaluation. We find that, surprisingly, the
corrections of the "squared decay-rate type" are the numerically dominant
contributions in the order (alpha/pi)^2 (Z alpha)^6 m_e c^2 for states with
large angular momenta, and provide an estimate of the entire B_60-coefficient
for Rydberg states with high angular momentum quantum numbers. Our results
reach the predictive limits of the quantum electrodynamic theory of the Lamb
shift.
