Higher-order hadronic contributions to the anomalous magnetic moment o
f the electron, muon, and tau lepton are considered in detail. As a ma
in result we find a reduction by -11 x 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 em
ploy the method of asymptotic expansions to calculate kernel functions
analytically in terms of a series expansion in the lepton mass.