We have studied excitation energy transfer in the photosynthetic antenna systems LH1 and LH2 of purple bacteria. Femtosecond pump-probe experiments are combined with computer simulations using the recently established crystal structure of these systems to assess the nature of excitation motion. We have measured the transient absorption kinetics and spectra of the LH1 and LH2 complexes in the temperature range from 4.2 to 296 K with femtosecond time resolution. The calculations based on the Pauli master equation disagreed with experimentally measured population and anisotropy kinetics, suggesting that the simple model of excitation hopping between bacteriochlorophyll a molecules is not a proper description for energy transport in LH1 and LH2. As a next step we have used the exciton theory to reproduce the transient absorption spectra of LH2, and we found that the coherence length of the exciton in B850 of LH2 1.5 ps after excitation of B800 is 4 +/- 1.