  Higher-order hadronic contributions to the anomalous magnetic moment of the
electron, muon, and $\tau$ lepton are considered in detail. As a main result we
find a reduction by $-11 \times 10^{-11}$ for the g-2 of the muon as compared
to previous calculations. Analytical expressions for the kernel functions of
higher-order hadronic effects are presented. We employ the method of asymptotic
expansions to calculate kernel functions analytically in terms of a series
expansion in the lepton mass.
