The excited-state dynamics of the peripheral light-harvesting complex LH2 (B800-850) of Rb. sphaeroides is compared to that of the dimer subunit (B8200(OG)) of the core antenna complex LH1 of Rs. rubrum G9 at liquid helium temperatures by means of spectral hole burning. Both the B800 band of the LH2 complex and the absorption band of the B820(OG) subunit are inhomogeneously broadened. The homogeneous line width, GAMMA(hom), of B800 is determined by energy transfer within the LH2 complex (tau(transfer almost-equal-to 0.8 to 2.5 ps); it is temperature independent between 1.2 and 30 K and a factor of about 60 larger than that of B820(OG). By contrast, for B820(OG) GAMMA(hom) is only approximately 1 GHz at 1.2 K; it depends on temperature and is predominantly given by pure dephasing.